1. (12 points) For each of the following cases, give the expected value of the s
ID: 3370513 • Letter: 1
Question
1. (12 points) For each of the following cases, give the expected value of the statistic (the sample mean, ž, or the sample proportion, p), give the variance of the statistic, and tell whether the sampling distribution of the statistic is exactly normal, o approximately normal, or o not even approximately normal. a. X comes from a Poisson distribution with 2 1.4 per minute and L 5.0 minutes. The sample mean, , is calculated from a sample of size n 25. X comes from a binomial distribution with n = 40 and ?-0.16. The sample mean, i, is calculated from a sample of size n 3 of these binomial Xs. b. X comes from a normal distribution with ?-50 and ?2-120. calculated from a sample of size n 9. The sample mean, x, is c. The Xs are Yes/No Bernoulli random variables. sample proportion, p. 75. So, the sample mean is the same as th The population proportion is ? = 0.94 and the sample size is n = d.Explanation / Answer
(a) X follows the approximately Poisson distribution with the lambda=1.4per minute and L=5.0 minutes. The sample mean x_bar is calculated from a sample of size n=25,
then it is not even approximately normal.
(b) approximately normal
(c) Exactly normal
(d) not even approximately normal
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