If Xis a r.v. with mean u and variance o2, using Chebyshev's-Inequality, PX-H 20) S (a) 0.5 (b) 0.05 (c)0.657 (d) 0.25.

The waiting time T at a bank teller’s window between two successive customers isdistributed as exponential with a mean of four minutes. Find the following probabilities:(a) P(T ≥ 5, (b) P(3 ≤ T ≤ 6), (c) P(T ≤ 4), and (d) P(T < 5). NOTE: Please explain each part, so the problem can be used as a Study Guide

Suppose that the average height of men in the United States is approximately normallydistributed with a mean of approximately 70 inches and a standard deviation ofapproximately 4 inches. (a) If you take a sample of 4 men, find Pr {68 ≤ Y̅ ≤ 73}, the probability that the sample mean Y̅ will be between 68 and 73 inches. (b) If you take a sample of 16 men, find Pr {68 ≤ Y̅ ≤ 73}, the probability that the sample mean Y̅ will be between 68 and 73 inches. (c) If you take a sample of n men where n > 16, which one of the following is true? (circle one of the three statements.)Pr{68 ≤ Y̅ ≤ 73} > the probability that you found in (b)Pr{68 ≤ Y̅ ≤ 73} = the probability that you found in (b)Pr{68 ≤ Y̅ ≤ 73} < the probability that you found in (b)

4. Suppose you are given the following information: = 49.6870 – 2.1586X; r2 = 0.9757 (0.7463) (0.12113) df=8 T= (66.578) (-17.821) p-value = (0.000) (0.000) a) Conduct a two tailed hypothesis test that: i) The intercept is 49 and the slope coefficient is -2, use 1% significance. ii) Confirm your deductions to 4(a) (i) using a confidence interval approach b) What does the r2 tell you? c) Perform a hypothesis using r2, such that p=D0, what do you conclude?

25. Each of a random sample of 30 student nurses who participated in a research project was given a  test designed to measure the degree of creative thinking. The standard deviation of the scores was 11. Can one conclude from these data that the population variance is less than 400?   Let α = 0. 05 and assume that the population is normally distributed.  (A) Yes (B) No

52. Multiple Choice If the calorie contents of robin eggs are normally distributed with a mean of 25 and a standard devia- tion of 1.2, then approximately 95% of all robin eggs should In have a calorie content in the interval ex (A) [21.4, 28.6]. (B) [22, 28]. (C) [22.6, 27.4]. (D) [23, 27]. (E) [23.8, 26.2].

5. Suppose the number of days it takes you to get a flu shot after it is available follows this equation: Y₂ = 30 - 2X₁ where y, is the number of days until you get the flu shot, and X, is the number of people you know who have the flu. Further, suppose on average you know 2.3 people who have the flu, with standard deviation 5. Suppose that the population has size m = 10. (a) Find the average time until you get the flu shot after it is available. (b) Find the standard deviation of time until you get the flu shot after it is available. (c) What is EY;?

3. Suppose that X has an exponential distribution with a mean of 10. Determine the following: (a) P(X 15) (c) Compare the results in parts (a) and (b) and comment on the role of memoryless property.

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