Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 4, Problem 108SE
An oocyte is a female germ cell involved in reproduction. Based on analyses of a large sample, the article “Reproductive Traits of Pioneer Gastropod Species Colonizing Deep-Sea Hydrothermal Vents After an Eruption” (Marine Biology, 2011: 181–192) proposed the following mixture of
f(x) = pf1(x; µ1, σ) + (1 − p) f2(x; µ2, σ)
where f1 and f2 are normal pdfs. Suggested parameter values were p = .35, µ1 = 4.4, µ2 = 5.0, and σ = .27.
a. What is the expected (i.e. mean) value of oocyte diameter?
b. What is the
c. What is the probability that oocyte diameter is smaller than its
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The article "Characteristics and Trends of River Discharge into Hudson, James, and Ungava
Bays, 1964-2000" (S. Dery, M. Stieglitz, et al., Journal of Climate, 2005:2540-2557)
presents measurements of discharge rate x (in kmlyr) andpeakflow y (in m/s) for 42 rivers
that drain into the Hudson, James, and Ungava Bays. The data are shown in the following
table:
Discharge
Peak Flow
94.24
4110.3
66.57
4961.7
59.79
10275.5
48.52
6616.9
40.00
7459.5
32.30
2784.4
31.20
3266.7
30.69
4368.7
26.65
1328.5
22.75
4437.6
21.20
1983.0
20.57
1320.1
19.77
1735.7
18.62
1944.1
17.96
3420.2
17.84
2655.3
16.06
3470.3
1561.6
14.69
11.63
869.8
11.19
936.8
11.08
1315.7
10.92
1727.1
9.94
768.1
7.86
483.3
Total plasma volume is Important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall
health and physical activity of an individual. Suppose that a random sample of 46 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg
(milliliters plasma per kilogram body weight). Assume that o = 7.40 ml/kg for the distribution of blood plasma.
(a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.)
lower limit
upper limit
margin of error
(b) What conditions are necessary for your calculations? (Select all that apply.)
On is large
O the distribution of volumes is uniform
Oo is known
o is unknown
the distribution of volumes is normal
(c) Interpret your results in the context of this problem.
O We are 1% confident that the true average blood plasma…
Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 44 male firefighters are tested and
that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight), Assume that o = 8.00 ml/kg for the distribution of blood plasma.
Chapter 4 Solutions
Probability and Statistics for Engineering and the Sciences
Ch. 4.1 - The current in a certain circuit as measured by an...Ch. 4.1 - Suppose the reaction temperature X (in C) in a...Ch. 4.1 - The error involved in making a certain measurement...Ch. 4.1 - Let X denote the vibratory stress (psi) on a wind...Ch. 4.1 - A college professor never finishes his lecture...Ch. 4.1 - The actual tracking weight of a stereo cartridge...Ch. 4.1 - The article Second Moment Reliability Evaluation...Ch. 4.1 - Prob. 8ECh. 4.1 - Based on an analysis of sample data, the article...Ch. 4.1 - A family of pdfs that has been used to approximate...
Ch. 4.2 - Let X denote the amount of time a book on two-hour...Ch. 4.2 - The cdf for X (= measurement error) of Exercise 3...Ch. 4.2 - Prob. 13ECh. 4.2 - The article Modeling Sediment and Water Column...Ch. 4.2 - Let X denote the amount of space occupied by an...Ch. 4.2 - The article A Model of Pedestrians Waiting Times...Ch. 4.2 - Let X have a uniform distribution on the interval...Ch. 4.2 - Let X denote the voltage at the output of a...Ch. 4.2 - Let X be a continuous rv with cdf...Ch. 4.2 - Consider the pdf for total waiting time Y for two...Ch. 4.2 - An ecologist wishes to mark off a circular...Ch. 4.2 - The weekly demand for propane gas (in 1000s of...Ch. 4.2 - If the temperature at which a certain compound...Ch. 4.2 - Let X have the Pareto pdf f(x;k,)={kkxk+1x0x...Ch. 4.2 - Let X be the temperature in C at which a certain...Ch. 4.2 - Let X be the total medical expenses (in 1000s of...Ch. 4.2 - Prob. 27ECh. 4.3 - Let Z be a standard normal random variable and...Ch. 4.3 - In each case, determine the value of the constant...Ch. 4.3 - Find the following percentiles for the standard...Ch. 4.3 - Determine z for the following values of : a. =...Ch. 4.3 - Suppose the force acting on a column that helps to...Ch. 4.3 - Mopeds (small motorcycles with an engine capacity...Ch. 4.3 - The article Reliability of Domestic-Waste Biofilm...Ch. 4.3 - In a road-paving process, asphalt mix is delivered...Ch. 4.3 - Spray drift is a constant concern for pesticide...Ch. 4.3 - Suppose that blood chloride concentration (mmol/L)...Ch. 4.3 - There are two machines available for cutting corks...Ch. 4.3 - The defect length of a corrosion defect in a...Ch. 4.3 - The article Monte Carlo SimulationTool for Better...Ch. 4.3 - The automatic opening device of a military cargo...Ch. 4.3 - The temperature reading from a thermocouple placed...Ch. 4.3 - Vehicle speed on a particular bridge in China can...Ch. 4.3 - If bolt thread length is normally distributed,...Ch. 4.3 - A machine that produces ball bearings has...Ch. 4.3 - The Rockwell hardness of a metal is determined by...Ch. 4.3 - The weight distribution of parcels sent in a...Ch. 4.3 - Suppose Appendix Table A.3 contained (z) only for...Ch. 4.3 - Consider babies born in the normal range of 3743...Ch. 4.3 - In response to concerns about nutritional contents...Ch. 4.3 - Chebyshevs inequality, (see Exercise 44, Chapter...Ch. 4.3 - Let X denote the number of flaws along a 100-m...Ch. 4.3 - Let X have a binomial distribution with parameters...Ch. 4.3 - Suppose that 10% of all steel shafts produced by a...Ch. 4.3 - Suppose only 75% of all drivers in a certain state...Ch. 4.3 - Show that the relationship between a general...Ch. 4.3 - a. Show that if X has a normal distribution with...Ch. 4.3 - There is no nice formula for the standard normal...Ch. 4.4 - Let X = the time between two successive arrivals...Ch. 4.4 - Let X denote the distance (m) that an animal moves...Ch. 4.4 - Data collected at Toronto Pearson International...Ch. 4.4 - The article Microwave Observations of Daily...Ch. 4.4 - A consumer is trying to decide between two...Ch. 4.4 - Evaluate the following: a. (6) b. (5/2) c. F(4; 5)...Ch. 4.4 - Let X denote the data transfer time (ms) in a grid...Ch. 4.4 - The two-parameter gamma distribution can be...Ch. 4.4 - Suppose that when a transistor of a certain type...Ch. 4.4 - The special case of the gamma distribution in...Ch. 4.4 - A system consists of five identical components...Ch. 4.4 - If X has an exponential distribution with...Ch. 4.4 - a. The event {X2 y} is equivalent to what event...Ch. 4.5 - The lifetime X (in hundreds of hours) of a certain...Ch. 4.5 - The authors of the article A Probabilistic...Ch. 4.5 - Prob. 74ECh. 4.5 - Let X have a Weibull distribution with the pdf...Ch. 4.5 - The article The Statistics of Phytotoxic Air...Ch. 4.5 - Prob. 77ECh. 4.5 - The article On Assessing the Accuracy of Offshore...Ch. 4.5 - Nonpoint source loads are chemical masses that...Ch. 4.5 - a. Use Equation (4.13) to write a formula for the...Ch. 4.5 - Sales delay is the elapsed time between the...Ch. 4.5 - As in the case of the Weibull and Gamma...Ch. 4.5 - What condition on and is necessary for the...Ch. 4.5 - Suppose the proportion X of surface area in a...Ch. 4.5 - Let X have a standard beta density with parameters...Ch. 4.5 - Stress is applied to a 20-in. steel bar that is...Ch. 4.6 - The accompanying normal probability plot was...Ch. 4.6 - A sample of 15 female collegiate golfers was...Ch. 4.6 - Prob. 89ECh. 4.6 - The article A Probabilistic Model of Fracture in...Ch. 4.6 - Construct a normal probability plot for the...Ch. 4.6 - The article The Load-Life Relationship for M50...Ch. 4.6 - Prob. 93ECh. 4.6 - The accompanying observations are precipitation...Ch. 4.6 - Use a statistical software package to construct a...Ch. 4.6 - Prob. 96ECh. 4.6 - The following failure time observations (1000s of...Ch. 4 - Let X = the time it takes a read/write head to...Ch. 4 - Prob. 99SECh. 4 - Let X denote the time to failure (in years) of a...Ch. 4 - The completion time X for a certain task has cdf...Ch. 4 - Let X represent the number of individuals who...Ch. 4 - The article Computer Assisted Net Weight...Ch. 4 - When circuit boards used in the manufacture of...Ch. 4 - Prob. 105SECh. 4 - The reaction time (in seconds) to a certain...Ch. 4 - Let X denote the temperature at which a certain...Ch. 4 - An oocyte is a female germ cell involved in...Ch. 4 - Prob. 109SECh. 4 - Prob. 110SECh. 4 - Prob. 111SECh. 4 - The article Error Distribution in Navigation (J....Ch. 4 - Prob. 113SECh. 4 - Suppose a particular state allows individuals...Ch. 4 - Let Ii be the input current to a transistor and I0...Ch. 4 - Prob. 116SECh. 4 - Prob. 117SECh. 4 - a. Suppose the lifetime X of a component, when...Ch. 4 - Prob. 119SECh. 4 - Prob. 120SECh. 4 - The article Three Sisters Give Birth on the Same...Ch. 4 - Let X denote the lifetime of a component, with f...Ch. 4 - Prob. 123SECh. 4 - Prob. 124SECh. 4 - A function g(x) is convex if the chord connecting...Ch. 4 - Let X have a Weibull distribution with parameters ...Ch. 4 - An individuals credit score is a number calculated...Ch. 4 - Prob. 128SE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- An article in the Fire Safety Journal (“The Effect of Nozzle Design on the Stability and Performance of Turbulent Water Jets,” Vol. 4, August 1981) describes an experiment in which a shape factor was determined for several different nozzle designs at six levels of jet efflux velocity. Interest focused on potential differences between nozzle designs (blocks), with velocity considered as a nuisance variable. The data are shown below: Jet Efflux Velocity (m/s) Nozzle Design 11.73 14.37 16.59 20.43 23.46 28.74 1 0.78 0.80 0.81 0.75 0.77 0.78 2 0.85 0.85 0.92 0.86 0.81 0.83 3 0.93 0.92 0.95 0.89 0.89 0.83 4 1.14 0.97 0.98 0.88 0.86 0.83 5 0.97 0.86 0.78 0.76 0.76 0.75 1) Write the null hypothesis and the alternative hypothesis (for the factor). 2) Find the ANOVA table. (round to five decimal places). 3) What is your decision about the null hypothesis, consider ?. 4) If your decision in part (4) was reject , perform Tukey test to determine which pairwise means are…arrow_forwardTotal plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 44 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that o = 7.40 ml/kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit upper limit margin of error (b) What conditions are necessary for your calculations? (Select all that apply.) O the distribution of volumes is uniform O the distribution of volumes is normal O o is unknown O n is large O o is known (c) Interpret your results in the context of this problem. O we are 99% confident that the true average blood…arrow_forwardThe efficiency ratio for a steel specimen immersed in a phosphating tank is the weight of the phosphate coating divided by the metal loss (both in mg/ft2). The article “Statistical Process Control of a Phosphate Coating Line” (Wire J. Intl., May 1997: 78–81) gave the accompanying data on tank temperature (x) and efficiency ratio (y).Temp. 170 172 173 174 174 175 176Ratio .84 1.31 1.42 1.03 1.07 1.08 1.04Temp. 177 180 180 180 180 180 181Ratio 1.80 1.45 1.60 1.61 2.13 2.15 .84Temp. 181 182 182 182 182 184 184Ratio 1.43 .90 1.81 1.94 2.68 1.49 2.52Temp. 185 186 188Ratio 3.00 1.87 3.08a. Construct stem-and-leaf displays of both temperature and efficiency ratio, and comment on interesting features.b. Is the value of efficiency ratio completely and uniquely determined by tank temperature? Explain your reasoning.c. Construct a scatterplot of the data. Does it appear that efficiency ratio could be very well predicted by the value of temperature? Explain your reasoning.arrow_forward
- An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.11 kgf/cm² for the modified mortar (m = 42) and y = 16.82 kgf/cm² for the unmodified mortar (n = 30). Let μ₁ and μ₂ be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (a) Assuming that ₁ = 1.6 and ₂ = 1.3, test Ho: ₁ - ₂ = 0 versus H₂ : ₁ - ₂ > 0 at level 0.01. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. O Reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds 0. O Fail to reject Ho. The data does not suggest that the difference in average tension bond strengths…arrow_forwardThe article “Stochastic Estimates of Exposure and Cancer Risk from Carbon Tetrachloride Released to the Air from the Rocky Flats Plant” (A. Rood, P. McGavran, et al., Risk Analysis, 2001:675–695) models the increase in the risk of cancer due to exposure to carbon tetrachloride as lognormal with μ = −15.65 and σ = 0.79. a) Find the mean risk. b) Find the median risk. c) Find the standard deviation of the risk. d) Find the 5th percentile. e) Find the 95th percentile.arrow_forwardAn experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified mortar resulted in x = 18.11 kgf/cm² for the modified mortar (m = 42) and y = 16.82 kgf/cm² for the unmodified mortar (n = 32). Let μ₁ and μ₂ be the true average tension bond strengths for the modified and unmodified mortars, respectively. Assume that the bond strength distributions are both normal. (a) Assuming that 0₁ = 1.6 and ₂ = 1.3, test Ho: ₁ - ₂ = 0 versus H₂: M₁-M₂ > 0 at level 0.01. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. O Reject Ho. The data does not suggest that the difference in average tension bond strengths exceeds 0. O Fail to reject Ho. The data suggests that the difference in average tension bond strengths exceeds…arrow_forward
- Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 45 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that o = 8.00 ml/kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit upper limit margin of error (b) What conditions are necessary for your calculations? (Select all that apply.) O o is unknown O the distribution of volumes is uniform O the distribution of volumes is normal O n is large O o is known (c) Interpret your results in the context of this problem. O The probability that this interval contains the…arrow_forwardAn article in Journal of Food Science [“Prevention of Potato Spoilage During Storage by Chlorine Dioxide” (2001, Vol. 66(3), pp. 472–477)] reported on a study of potato spoilage based on different conditions of acidified oxine (AO), which is a mixture of chlorite and chlorine dioxide. The data follow: ∑X1i=230, ∑X21i=17200, n1=3. ∑X2i=150, ∑X22i=8100, n2=3. ∑X3i=60, ∑X23i=4500, n3=3. ∑X4i=65, ∑X24i=1625, n4=3. where group 1 has AO = 50ppm, group 2 has AO = 100ppm, group 3 has AO = 200ppm, group 4 has AO = 400ppm. Complete the ANOVA table below Source df sum of square mean square F p-value Between Within N/A N/A Total 11 N/A N/A N/A At α=0.05, do we reject the null hypothesis that AO does not affect spoilage?arrow_forwardWhat type of model is presented below – Model 3. What impact do d_y and d_rs have on the dependent variable d_m_p? Model 3: OLS, using observations 1980:2-1999:3 (T = 78) Dependent variable: d_m_p Coefficient Std. Error t-ratio p-value const 0.0113971 0.00130078 8.7617 <0.0001 *** d_y −0.0106911 0.100221 −0.1067 0.9153 d_rs 0.00151462 0.00110613 1.3693 0.1751 d_rl 0.000127744 0.00141954 0.0900 0.9285 d_p −0.354204 0.093535 −3.7869 0.0003 *** Mean dependent var 0.007578 S.D. dependent var 0.004753 Sum squared resid 0.001399 S.E. of regression 0.004378 R-squared 0.195607 Adjusted R-squared 0.151531 F(4, 73) 4.437922 P-value(F) 0.002885 Log-likelihood 315.5363 Akaike criterion −621.0725 Schwarz criterion −609.2890 Hannan-Quinn −616.3554 rho 0.485424 Durbin-Watson 1.001216arrow_forward
- Riboflavin (Vitamin B2) is determined in a cereal sample by measuring its fluorescence intensity(형광세기) in 5% acetic acid solution. A calibration curve was prepared by measuring the fluorescence intensities of a series of standards of increasing concentrations. The following data were obtained. Riboflavin (μg/mL) 0.000 0.100 0.200 0.400 0.800 Unknown sample Fluorescence intensity 0.0 5.8 12.2 22.3 43.3 15.4 (a) Use the method of least squares to obtain the best straight line through these five points (n=5). (b) Make a graph showing the experimental data and the calculated straight line. (c) An unknown sample gave an observed fluorescence intensity of 15.4. Calculate the concentration of Riboflavin (Vitamin B2) in the unknown sample (μg/mL). (d) Calculate the coefficient of determination (R2).arrow_forwardFifty male subjects drank a measured amount x (in ounces) of a medication and the concentration y (in percent) in their blood of the active ingredient was measured 30 minutes later. The sample data are summarized by the following information: n = 50 Ex = 112.5 Ex? = 356.25 %3D Ey = 4.83 Ey = 0.667 Exy = 15.255 0 < x < 4.5 Or= 0.875 Or= 0.709 Or= -0.846 Or=0.460 Or= 0.965arrow_forwardTotal plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 48 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.10 ml/kg for the distribution of blood plasma. (a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error? (Round your answers to two decimal places.) lower limit upper limit margin of error (b) What conditions are necessary for your calculations? (Select all that apply.) n is largethe distribution of weights is uniformσ is knownthe distribution of weights is normalσ is unknown (c) Interpret your results in the context of this problem. We are 99% confident that the true…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Hypothesis Testing using Confidence Interval Approach; Author: BUM2413 Applied Statistics UMP;https://www.youtube.com/watch?v=Hq1l3e9pLyY;License: Standard YouTube License, CC-BY
Hypothesis Testing - Difference of Two Means - Student's -Distribution & Normal Distribution; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=UcZwyzwWU7o;License: Standard Youtube License