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In: Statistics and Probability

The length of time, in hours, it takes an "over 40" group of people to play...

The length of time, in hours, it takes an "over 40" group of people to play one soccer match is normally distributed with a mean of 2.2 hours and a standard deviation of 0.55 hours. A sample of size n = 80 is drawn randomly from the population. Find the probability that the sample mean is between 2.1 hours and 2.4 hours.

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Expert Solution

Solution :

Given that,

mean = = 2.2

standard deviation = = 0.55

= / n = 0.55 / 80 = 0.0615

= P[(2.1 - 2.2) /0.0615< ( - ) / < (2.4 - 2.2) / 0.0615)]

= P(-1.63 < Z < 3.25)

= P(Z < 3.25) - P(Z < -1.63)

= 0.9994 - 0.0516

= 0.9978

Probability = 0.9978

orchestra answered 2 years ago
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