Question

The IQ scores of adults are normally distributed with a mean 100 and a standard deviation of 15. If a group of 64 adults is randomly​ selected, what is the probability that their mean IQ will be at least​ 95? A. 0.6293 B. 0.3707 C. 0.9962 D. 0.0038

Answer 1

Answer

we have , n = sample size = 64

is population mean and is population standard deviation

we have to find the probability that the mean IQ for 64 adults will be at least 95

So, we have to find the value of P(at least 95)

Using the formula

where x(bar) = 95

setting the given values, we get

P(z > (95-100 ) // (15N64) P(z > (-5/(15/8)))-P(z >-2.667)

using identity

we can write it as

Using z distribution table to find the required p value (checking 2 on left most column and 0.667 on top most row), we get

P(z >-2.667) P(z < 2.667) = 0.9962

So, option C is correct answer