In: Statistics and Probability
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?
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