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 of 0.5 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. g

Answer 1

`P(\overline X < 2.3) = 0.9999`

Explanation:

Given that:

mean = 2

standard deviation = 0.5

sample size = 50

The probability that the sample mean is less than 2.3 hours is :

`P(\overline X < 2.3) = P(Z \leq (\overline x - \mu)/((\sigma)/(√(n))))`

`P(\overline X < 2.3) = P(Z \leq (2.3 - 2.0)/((0.5)/(√(50))))`

`P(\overline X < 2.3) = P(Z \leq (0.3)/(0.07071))`

`P(\overline X < 2.3) = P(Z \leq 4.24268)`

`P(\overline X < 2.3) = P(Z \leq 4.24)`

From z tables;

`P(\overline X < 2.3) = 0.9999`