Question

The length of time, in hours, it takes a group of people, 40 years and older, to play one soccer match is normally distributed with a mean of 2 hours and a standard deviation of0.5 hours. A sample of size 50 is drawn randomly from the population. Find the probability that the sample mean is less than 2.3 hours.

A.Write the probability in terms of the statistic.

B. Write the probability in terms of the z-score.

C.Write the probability in a numeric, decimal form.

Answer 1

ANSWER:

Length of time, X ~ N( = 2, = 0.5)

Standard error of sample mean, SE =   = 0.5 / = 0.0707

a).

Probability that sample mean is less than 2.3 hours =

P( < 2.3)

b).

z-score = (x - ) / SE = (2.3 - 2) / 0.0707 = 4.24

Probability in terms of z-score is,

P(Z < 4.24)

c).

Exact probability is,

P(Z < 4.24) = 0.9999888   

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