sider the next 1000 90% CIs for that a statistical consultant will obtain for va

Question

sider the next 1000 90% CIs for that a statistical consultant will obtain for various clients. Suppose the data sets on which the intervals are based are selected independently of one another. many of these 1000 intervals do you expect to capture the corresponding value of ? intervals what is the probability that between 890 and 910 of these intervals contain the corresponding value of ? [Hint: Let = the number among the 1000 intervals that contain . what kind of random variable is Y (Round your answer to four decimal places.)

Explanation / Answer

Set Y as the number of intervals capture . Then Y is following binomial distribution with parameters

n=1000 and p = 0.90.

E(Y) = n * p = 900

900 intervals

Var(Y) = np(1-p) = 90 and

sd(Y) = 9.49

Then using the central limit theorem and approximation modification of discrete distribution, we have

P(890 Y 910) = P(889.5 Y 910.5)

P(-1.11 Z 1.11) = 0.7330

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