Question

With a mean of 100 and a standard deviation of 15, a random sample of 100 IQ scores is selected. The probability that the sample mean is less than k is 85%. Find k.

Answer 1

Given,

= 100 , = 15

Using central limit theorem,

P( < x) = P( Z < x - / / sqrt(n) )

We have to calculate k such that

P( X < k) = 0.85

P( Z < k - / / sqrt(n) ) = 0.85

From Z table, z-score for the probability of 0.85 is 1.0364

So,

k - / / sqrt(n) = 1.0364

k - 100 / (15 / sqrt(100) ) = 1.0364

Solve for k

k = 101.5546