Question

In psychology, there is a particular Mental Development Index (MDI) used in the study of infants. The scores on the MDI have approximately a normal distribution with a mean of 100 and standard deviation of 16. We are going to randomly select 64 children and average their MDI scores. What is the probability that the average is greater than 102?

Answer 1

Solution :

Given that ,

mean = = 100

standard deviation = = 16

n = 64

= = 100

= / n = 16 / 64 = 2

P( >102 ) = 1 - P( < 102)

= 1 - P[( - ) / < (102-100) /2 ]

= 1 - P(z < 1)

= 1- 0.8413 = 0.1587

Probability = 0.1587