MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
expand_more
expand_more
format_list_bulleted
Related questions
Question
Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train. The
automatic hopper car loader is set to put 75 tons of coal into each car. The actual weight of coal loaded into
each car is
(a) There are 97% of the cars will be loaded with more than K tons of coal. What is the value of K?
(b) What is the
(c) Among 20 randomly chosen cars, what is the probability that more than 2 cars will be loaded with less
than 74.4 tons of coal?
(d) Among 20 randomly chosen cars, most likely, how many cars will be loaded with less than 74.4 tons of
coal? Calculate the corresponding probability.
(e) In the senior management meeting, it is discussed and agreed that a car loaded with less than 74.4 tons
of coal is not cost effective. To reduce the ratio of cars to be loaded with less than 74.4 tons of coal, it
is suggested changing current average loading of coal from 75 tons to a new average level, M tons.
Should the new level M be (I) higher than 75 tons or (II) lower than 75 tons? (Write down your
suggestion, no explanation is needed in part (e)).
Transcribed Image Text:The entries in Table I are the probabilities that a random variable having the
standard normal distribution will take on a value between 0 andz. They are given
by the area of the gray region under the curve in the figure.
TABLE I
NORMAL-CURVE AREAS
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.0
0.0000
0.0040
0.0080
0.0120
0.0160
0.0199
0.0239
0.0279
0.0319
0.0359
0.1
0.0398
0.0438
0.0478
0.0517
0.0557
0.0596
0.0636
0.0675
0.0714
0.0753
0.2
0.0793
0.0832
0.0871
0.0910
0.0948
0.0987
0.1026
0.1064
0.1103
0.1141
0.3
0.1179
0.1217
0.1255
0.1293
0.1331
0.1368
0.1406
0.1443
0.1480
0.1517
0.4
0.1554
0.1591
0.1628
0.1664
0.1700
0.1736
0.1772
0.1808
0.1844
0.1879
0.5
0.1915
0.1950
0.1985
0.2019
0.2054
0.2088
0.2123
0.2157
0.2190
0.2224
0.6
0.2257
0.2291
0.2324
0.2357
0.2389
0.2422
0.2454
0.2486
0.2517
0.2549
0.7
0.2580
0.2611
0.2642
0.2673
0.2704
0.2734
0.2764
0.2794
0.2823
0.2852
0.8
0.2881
0.2910
0.2939
0.2967
0.2995
0.3023
0.3051
0.3078
0.3106
0.3133
0.9
0.3159
0.3186
0.3212
0.3238
0.3264
0.3289
0.3315
0.3340
0.3365
0.3389
1.0
0.3413
0.3438
0.3461
0.3485
0.3508
0.3531
0.3554
0.3577
0.3599
0.3621
1.1
0.3643
0.3665
0.3686
0.3708
0.3729
0.3749
0.3770
0.3790
0.3810
0.3830
1.2
0.3849
0.3869
0.3888
0.3907
0.3925
0.3944
0.3962
0.3980
0.3997
0.4015
1.3
0.4032
0.4049
0.4066
0.4082
0.4099
0.4115
0.4131
0.4147
0.4162
0.4177
1.4
0.4192
0.4207
0.4222
0.4236
0.4251
0.4265
0.4279
0.4292
0.4306
0.4319
1.5
0.4332
0.4345
0.4357
0.4370
0.4382
0.4394
0.4406
0.4418
0.4429
0.4441
1.6
0.4452
0.4463
0.4474
0.4484
0.4495
0.4505
0.4515
0.4525
0.4535
0.4545
1.7
0.4554
0.4564
0.4573
0.4582
0.4591
0.4599
0.4608
0.4616
0.4625
0.4633
1.8
0.4641
0.4648
0.4656
0.4664
0.4671
0.4678
0.4685
0.4692
0.4699
0.4706
1.9
0.4713
0.4719
0.4725
0.4732
0.4738
0.4744
0.4750
0.4756
0.4761
0.4767
2.0
0.4772
0.4778
0.4783
0.4788
0.4793
0.4798
0.4803
0.4808
0.4812
0.4817
2.1
0.4821
0.4826
0.4830
0.4834
0.4838
0.4842
0.4846
0.4850
0.4854
0.4857
2.2
0.4861
0.4864
0.4868
0.4871
0.4875
0.4878
0.4881
0.4884
0.4887
0.4890
2.3
0.4893
0.4896
0.4898
0.4901
0.4904
0.4906
0.4909
0.4911
0.4913
0.4916
2.4
0.4918
0.4920
0.4922
0.4925
0.4927
0.4929
0.4931
0.4932
0.4934
0.4936
2.5
0.4938
0.4940
0.4941
0.4943
0.4945
0.4946
0.4948
0.4949
0.4951
0.4952
2.6
0.4953
0.4955
0.4956
0.4957
0.4959
0.4960
0.4961
0.4962
0.4963
0.4964
2.7
0.4965
0.4966
0.4967
0.4968
0.4969
0.4970
0.4971
0.4972
0.4973
0.4974
2.8
0.4974
0.4975
0.4976
0.4977
0.4977
0.4978
0.4979
0.4979
0.4980
0.4981
2.9
0.4981
0.4982
0.4982
0.4983
0.4984
0.4984
0.4985
0.4985
0.4986
0.4986
3.0
0.4987
0.4987
0.4987
0.4988
0.4988
0.4989
0.4989
0.4989
0.4990
0.4990
Also, for z = 4.0, 5.0 and 6.0, the areas are 0.49997, 0.4999997, and 0.499999999.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 4 steps
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
Transcribed Image Text:Let X be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood).
The distribution of X for a healthy person is normally distributed with men u = 85 and standard deviation o =
25. A person suffers from severe excess in insulin would have a lower level of glucose. A blood test with
result of X < 40 would be used as an indicator that medication is needed.
(a) What is the probability that a healthy person will be suggested with medication after a single test?
(b) A doctor uses the average result of 2 tests for diagnosis, that is X. The second test will be conducted
one week after the first test, so that the two test results are independent. For many healthy persons, each
has finished two tests, find the expectation and standard error of the distribution of X.
(c) The doctor suggests medication will be given only when the average level of glucoses in the 2 blood tests
is less than 40, that is X < 40, so to reduce the chance of unnecessary use of medication on a healthy
person. Use the distribution in part (b)) to find the probability that a healthy person will be suggested
with medication after 2 tests to verify this doctor's theory.
Solution
by Bartleby Expert
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
Transcribed Image Text:Let X be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood).
The distribution of X for a healthy person is normally distributed with men u = 85 and standard deviation o =
25. A person suffers from severe excess in insulin would have a lower level of glucose. A blood test with
result of X < 40 would be used as an indicator that medication is needed.
(a) What is the probability that a healthy person will be suggested with medication after a single test?
(b) A doctor uses the average result of 2 tests for diagnosis, that is X. The second test will be conducted
one week after the first test, so that the two test results are independent. For many healthy persons, each
has finished two tests, find the expectation and standard error of the distribution of X.
(c) The doctor suggests medication will be given only when the average level of glucoses in the 2 blood tests
is less than 40, that is X < 40, so to reduce the chance of unnecessary use of medication on a healthy
person. Use the distribution in part (b)) to find the probability that a healthy person will be suggested
with medication after 2 tests to verify this doctor's theory.
Solution
by Bartleby Expert
Knowledge Booster
Similar questions
- Ann thinks that there is a difference in quality of life between rural and urban living. She collects information from obituaries in newspapers from urban and rural towns in Idaho to see if there is a difference in life expectancy. A sample of 3 people from rural towns give a life expectancy of xr¯=79��¯=79 years with a standard deviation of sr=7.57��=7.57 years. A sample of 14 people from larger towns give xu¯=82��¯=82 years and su=5.48��=5.48 years. Does this provide evidence that people living in rural Idaho communities have different life expectancy than those in more urban communities? Use a 5% level of significance. (a) State the null and alternative hypotheses: (Type ‘‘mu_r′′‘‘��_�″ for the symbol μr�� , e.g. mu_rnot=mu_u��_����=��_� for the means are not equal, mu_r>mu_u��_�>��_� for the rural mean is larger, mu_r<mu_u��_�<��_� , for the rural mean is smaller. )H0�0 = equation editor Equation Editor Ha�� = equation editor Equation Editor (b) The degree of…arrow_forwardAfter visiting the Titanic, Captain Brain and Mr. Pinky are taking the Alvin submarine back to the surface of the water. They start 1900 meters below the surface of the water, and ascend at 62 meters per hour.Note: under the water is a negative number.Write an equation to model this situation (use mm for meters and hh for hours)arrow_forwardIn a large section of a statistics class, the points for the final exam are normally distributed, with a mean of 74 and a standard deviation of 8. Grades are assigned such that the top 10% receive A's, the next 20% received B's, the middle 40% receive C's, the next 20% receive D's, and the bottom 10% receive F's. Find the lowest score on the final exam that would qualify a student for an A, a B, a C, and a D. The lowest score that would qualify a student for an A is nothing. (Round up to the nearest integer as needed.) The lowest score that would qualify a student for a B is nothing. (Round up to the nearest integer as needed.) The lowest score that would qualify a student for a C is nothing. (Round up to the nearest integer as needed.) The lowest score that would qualify a student for a D is nothing. (Round up to the nearest integer as needed.)arrow_forward
- The average labor charge for automobile mechanics is OMR 69 per hour. The standard deviation is OMR 18. Find the minimum percentage of data values that will fall within the range of OMR 68 to OMR 80. Use Chebyshev's theorem. SHOW ALL THE WORKINGS, FORMULA etc.arrow_forwardThe reading speed of second grade students in a large city is approximately normal, with mean of 91 words per minute (wpm) and a standard deviation of 10 wpm. Complete parts (a) through (f). O B. If 100 different students were chosen from this population, we would expect to read exactly 95 words per minute. O C. If 100 different students were chosen from this population, we would expect to read less than 95 words per minute. (b) What is the probability that a random sample of 13 second grade students from the city results in a mean reading rate of more than 95 words per minute? The probability is 0.0746. (Round to four decimal places as needed.) Interpret this probability. Select the correct choice below and fill in the answer box within your choice. O A. If 100 independent samples of n = 13 students were chosen from this population, we would expect sample(s) to have a sample mean reading rate of exactly 95 words per minute. O B. If 100 independent samples of n = 13 students were…arrow_forwardThe height of men in country is normally distributed with mean of 6 feet and variance of 16 inches. What percentage the male population is between 72 and 76 inches in height?arrow_forward
- Suppose that the heights of adult men in the United States are normally distributed with a mean of 69 inches and a standard deviation of 3 inches. What proportion of adult men in the United States is at least 6 feet tall? (Hint 6 feet=72 inches.) Round answer to at least 4 decimal places.arrow_forwardIn a large section of a statistics class, the points for the final exam are normally distributed, with a mean of 73 and a standard deviation of 8. Grades are assigned such that the top 10% receive A's, the next 20% received B's, the middle 40% receive C's, the next 20% receive D's, and the bottom 10% receive F's. Find the lowest score on the final exam that would qualify a student for an A, a B, a C, and a D. Click here to view Page 1 of the Standard Normal Table. Click here to view Page 2 of the Standard Normal Table. The lowest score that would qualify a student for an A is (Round up to the nearest integer as needed.)arrow_forwardIn a large section of a statistics class, the points for the final exam are normally distributed, with a mean of 71and a standard deviation of 8. Grades are assigned such that the top 10% receive A's, the next 20% received B's, the middle 40% receive C's, the next 20% receive D's, and the bottom 10% receive F's. Find the lowest score on the final exam that would qualify a student for an A, a B, a C, and a D.arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning 
Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman