Question

In a large population of college-educated adullts, the IQ scores are normally distributed with a mean of 118 and standard deviation 20. Suppose 100 adults from this population are randomly selected for a market research campaign. The probability that the sample mean IQ is greater than 120 is closest to ________

Answer 1

0.1587 is the probability that the sample mean of 100 randomly selected adult's IQ is greater than 120.

Explanation:

We are given the following information in the question:

Mean, μ = 118

Standard Deviation, σ = 20

n = 100

We are given that the distribution of IQ scores is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/((\sigma)/(√(n)))`

P( IQ is greater than 120)

P(x > 120)

`P( x > 120) = P( z > \displaystyle(120 - 118)/((20)/(√(100)))) = P(z > 1)`

`= 1 - P(z \leq 1)`

Calculation the value from standard normal z table, we have,

`P(x > 120) = 1 - 0.8413 = 0.1587 = 15.87\%`

0.1587 is the probability that the sample mean of 100 randomly selected adult's IQ is greater than 120.