The ages of four students in a statistics class (considered the population) are:

Name Age

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Baker 24

Miller 19

Smith 22

Bailey 24

a. What is the shape of the population? (Graph the distribution)

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b. How many samples of size two are possible?

Solution

c. Select all possible samples of two and then compute the mean of each one.

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d. Organize the sample means into a sampling distribution. Compute the mean of the population and that of the sample means. Are these values the same?

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e. What is the shape of the sampling distribution? (graph it). What theorem explains the shape of this distribution?

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(2) A process that polishes a mirrored surface leaves an average of 2 small flaws per 5 m of surface. The number of flaws on an area of surface follows a Poisson distribution. a. What is the probability that a surface with area 3 m x 5 m will contain more than 5 flaws? b. What is the probability that a surface with area 2 m x 3 m will contain no flaws? c. What is the probability that 50 surfaces, each with dimensions 3 m x 6 m, will contain more than 350 flaws in total?Pick one of the choices O Inconsistent Consistent with infinitely many solutions Consistent with a unique solution None of the above Clear selection Probability & Statistics - Bernoulli Variables Let X1. Xz. .... Xing all be independent Bernoulli variables, which take a value of 1 with probability 0.5 Estimate the probability that X, + X2 + ... + X10