An article suggests the uniform distribution on the interval from 7.5 to 20 as a model for x = depth (in centimeters) of the bioturbation layer in sediment for a certain region. What is the height of the density curve? What is the probability that x is at most 16? P(x ≤ 16) = What is the probability that x is between 14 and 18? P(14 ≤ x ≤ 18) = What is the probability that x is between 13 and 17? P(13 ≤ x ≤ 17) =

I. Say true or false. The area under a Probability density function is close to 1. a) b) The mean and variance of normal distribution are 0 and 1 respectively. _The chi-square is a special kind of gamma distribution with a = v/2 and B=3. _The Beta distribution is a special kind of Uniform distribution. _The small sample size imply less error in the estimation of a c) d) e) parameter. _If Variable Y is distributed Chis-square with 10 degrees of freedom, its variance is 5. If the sample size increase the width of the Confidence interval decreases. The standard Beta distribution is defined in the interval a to b. f) g) h) i) _If we can identify the value of the parameters of a gamma distributed function. we can evaluate the mean and variance of the distribution. j) If value of A =20 and B = 30 of a uniform distribution then the mean of the distribution is 28. _Type I error and type II error may increase as the sample size k) decrease. As B increase the power of the test increase. _Type I…

A. P(t10>1.75), where t10 has a t distribution with 10 degrees of freedom

Central High School believes their students have unusually high SAT scores on average. The school has 165 students.Based on national data, the average SAT score is 1067 with a population standard deviation of 207. Assume SAT scores are normally distributed. Let X be the random variable representing the mean SAT scores for groups of 165 randomly selected students.a. Fill in the blank, rounding your answers to 2 decimal places if needed. According to the Central Limit Theorem, X is approximately normal with a mean of  and a standard error of the mean  .b. Find the z-score associated to a sample with a mean of 1109, using the sampling distribution. Round your answer to two decimal places. c. Find the probability that a randomly selected sample of 165 students has a mean SAT score higher than 1109. Round your answer to 4 decimal places. d. Central High School finds that for their students, the average SAT score is 1109. Are they justified in saying their students perform unusually well on…

Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for metal sheets of a particular type, its mean value and standard deviation are 70 GPa and 2.4 GPa, respectively. Suppose the distribution is normal. (Round your answers to four decimal places.) n USE SALT (a) Calculate P(69 < XS 71) when n = 25. (b) How likely is it that the sample mean diameter exceeds 71 when n = 49?

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The lengths of a professor's classes has a continuous uniform distribution between 49.2 min and 55.5 min. One class is randomly selected. If P(x > c) = 0.569 , find c. C = minutes (Report answer accurate to 4 decimal places.)

Assume that the amounts of weight that male college students gain during their freshman year are normally distributed with a mean of μ = 1.1 kg and a standard deviation of o= 5.6 kg. Complete parts (a) through (c) below. ... a. If 1 male college student is randomly selected, find the probability that he gains between 0 kg and 3 kg during freshman year. The probability is (Round to four decimal places as needed.)

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Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy females, x has an approximately normal distribution with mean u - 5.3 and standard deviation a - 0.7. The Standard Normal Distribution u = 0, o = 1) -1 68% of area 95% of area 99.7% of area (a) Convert the x interval, 4.5 < x, to a z interval. (Round your answer to two decimal places.) (b) Convert the x interval, x < 4.2, to a z interval. (Round your answer to two decimal places.) z< (c) Convert the x interval, 4.0 < x< 5.5, to a z interval. (Round your answers to two decimal places.)