Question

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 4 hours and a standard deviation of 0.5 hours. A sample of size n = 50 is drawn randomly from the population. Find the probability that the sample mean is between 3.5 hours and 4.1 hours.

Answer 1

SOLUTION:

From given data,

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 4 hours and a standard deviation of 0.5 hours. A sample of size n = 50 is drawn randomly from the population.

standard deviation = = 0.5

sample size = n = 50

mean = = 4

Z = - /

Where,

= = 4

= / sqrt(n) = 0.5/sqrt(50) = 0.07071

Z = - 4 / 0.07071

Find the probability that the sample mean is between 3.5 hours and 4.1 hours.

At = 3.5

Z = 3.5 - 4 / 0.07071

Z = -7.07

At = 4.1

Z = 4.1 - 4 / 0.07071

Z = 1.41

P(3.5 < < 4.1) = P(-7.07 < Z < 1.41)

P(3.5 < < 4.1) = P(Z ​​​​​​​ < 1.41) - P(Z ​​​​​​​ < -7.07)

P(3.5 < < 4.1) = 0.92073 - 0

P(3.5 < < 4.1) = 0.92073