Question

3) The average age of students at XYZ University is 24 years with a standard deviation of 8 years. Number of students at the university is 7500. A random sample of 36 students is selected. What is the probability that the sample mean will be between 25.5 and 27 years

Answer 1

0.1875

Explanation:

σM=σ/√N

=8/√7500

=8/86.608

=0.092

Z=(x-μ)/σ/√N

=(25.5-36)/8/√7500

=-10.5/0.0092=-1141.304

Z score = -1.3125

=(27-36)/8/√7500 =

=9/0.0092=978.261

Z score= -1.125

-1.125-(-1.3125)=-1.125+1.3125)= 0.1875

The probability that the sample mean will be between 25.5 and 27 years

P(between 25.5 and 27) = 0.1875