The Mental Development Index MDI of the Bayley Scales of Inf

The Mental Development Index (MDI) of the Bayley Scales of Infant Development is a standardized measure used in longitudinal follow-up of high-risk infants. The scores on the MDI have approximately a normal distribution with a mean of 100 and standard deviation of 16. What proportion of children have MDI of at least 80?

Solution

The probability is

P(xbar<105) = P((xbar-mean)/(s/vn) <(105-100)/(16/8))

=P(Z<2.5)

=0.9938 (from standard normal table)