Question

The Intelligence Quotient (IQ) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 25. What is the probability we could select a sample of 80 adults and find the mean of this sample is between 95 and 105

Answer 1

The probability is 0.6796

Explanation:

Given

Population Mean - 100

Population Standard Deviation - 25

As we know

z = x-μ/σ, where:

z is the standard score

x is the raw score

μ is the population mean

σ is the population standard deviation

Z value for mean of sample = 95

z1 = -100+95/25 = -5/25 = -0.2

P value for Z = -0.2 is 0.2912

Z2 = 100-105/25 = 0.2

P(z > 0.2 = 1 - P(z ≤ 0.2) = 1 - 0.0294 = 0.9706

P(-0.2 < z < 0.2) = 0.9706 - 0.2912= 0.6796

The probability is 0.6796