Question

The population of IQ scores forms a normal distribution with mu equals space 100 and sigma space equals space 15. If you take a random sample of 25 people who have taken the IQ test, what is the probability of obtaining a sample mean greater than M = 94?

Answer 1

Solution :

Given that ,

mean = = 100

standard deviation = = 15

n = 25

= = 100 and

= / n = 15 / 25 = 3

P( > 94) = 1 - P( < 94)

= 1 - P(( - ) / < (94 - 100) / 3)

= 1 - P(z < -2)

= 1 - 0.0228 Using standard normal table.

= 0.9772

Probability = 0.9772