Question

# A random sample of n = 81 observations is drawn from a population with a mean...

A random sample of n = 81 observations is drawn from a population with a mean equal to 15 and a standard deviation equal to 9 . Complete parts a through g below. a. Give the mean and standard deviation of the? (repeated) sampling distribution x overbar . mu Subscript x overbar equalsnothingsigma Subscript x overbar equalsnothing ?(Type integers or? decimals.) b. Describe the shape of the sampling distribution of x overbar . Does this answer depend on the sample? size? Choose the correct answer below. A. The shape is that of a normal distribution and depends on the sample size. B. The shape is that of a uniform distribution and does not depend on the sample size. C. The shape is that of a normal distribution and does not depend on the sample size. D. The shape is that of a uniform distribution and depends on the sample size. c. Calculate the standard normal? z-score corresponding to a value of x overbar equals17.0 . zequals nothing ?(Type an integer or a? decimal.) d. Calculate the standard normal? z-score corresponding to a value of x overbar equals20.4 . zequals nothing ?(Type an integer or a? decimal.) e. Find Upper P left parenthesis x overbar less than 17.0 right parenthesis . Upper P left parenthesis x overbar less than 17.0 right parenthesis equalsnothing ?(Round to four decimal places as? needed.) f. Find Upper P left parenthesis x overbar greater than 20.4 right parenthesis . Upper P left parenthesis x overbar greater than 20.4 right parenthesis equalsnothing ?(Round to four decimal places as? needed.)

a) = 15

b) Option - A) The shape is that of a normal distribution and depends on the sample size.

c)

d)

e) P( < 17)

= P(Z < 2)

= 0.9772

f) P( > 20.4)

= P(Z > 5.4)

= 1 - P(Z < 5.4)

= 1 - 1 = 0

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