Question

A typical adult has an average IQ score of 105 with a standard deviation of 20. If 20 randomly selected adults are given an IQ test, what is the probability that the sample mean scores will between 102 and 110 points? (Round to 2 decimal places)

Answer 1

Answer: 0.55

Step-by-step explanation:

Given :

A typical adult has an average IQ score of n $\mu=105$ with a standard deviation $\sigma=20$.

Sample size : n= 20

Let x represents the IQ score of adults.

The probability that the sample mean scores will between 102 and 110 points will be :-

$P(102<x<110)=P(\dfrac{102-105}{20}< \dfrac{x-\mu}{\sigma}<\dfrac{110-105}{20})\\\\=P(-0.15<z<0.25)\\\\=P(z<0.25)-P(z<-0.15)\\\\=P(z<0.25)-(1-P(z<0.15))\\\\=0.9937903-(1-0.5596177)=0.553408\approx0.55$

Therefore, the probability that the sample mean scores will between 102 and 110 points = 0.55