Question

Question #8: The score of the LSAT examination have a population mean µ = 70 and population standard deviation σ = 10. Answer the questions below and show work.

1.) A random sample of 64 individuals is taken. What is the probability that the sample mean is below 71?
2.) A random sample of 100 individuals is taken. What is the probability that the sample mean is below 71?

Answer 1

8)

Solution :

1)

= / n = 10 / 64 =  1.25

P( < 71) = P(( - ) / < (71 - 70) / 1.25)

= P(z < 0.8)

=  0.7881

Probability = 0.7881

2)

= / n = 10 / 100 =  1

P( < 71) = P(( - ) / < (71 - 70) / 1)

= P(z < 1)

=  0.8413

Probability = 0.8413