Question

An index that is a standardized measure used in observing infants over time is approximately normal with a mean of 93 and a standard deviation of 5.

a. What proportion of children have an index of​ (i) at least 113​? ​(ii) at least 78​?

Answer 1

Given that, mean (μ) = 93 and standard deviation = 5

Let X ~ N(93, 5)

a) Using standard normal z-table we find the following proportions,

i) We want to find, P(X ≥ 113)

Therefore, the proportion of children have an index of at least 113 is 0.0000

ii) We want to find, P(X ≥ 78)

Therefore, the proportion of children have an index of at least 78 is 0.9987