Question

A normal distribution has \mu = 65 and \sigma = 10. Find the probability that the average score of a group of n = 4 people is between 70 and 75 (both limits included).

Answer 1

Answer:

The probability that the average score of a group of n = 4 people is between 70 and 75=0.13591

Step-by-step explanation:

We are given that

$\mu=65$

$\sigma=10$

n=4

We have to find the probability that the average score of a group of n = 4 people is between 70 and 75.

$P(70<\bar{x}<75)=P(\frac{70-65}{\frac{10}{\sqrt{4}}}<\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}<\frac{75-65}{\frac{10}{\sqrt{4}}})$

$=P(\frac{5}{5}<Z<\frac{10}{5})$

$=P(1<Z<2)$

$=P(Z<2)-P(Z<1)$

$=0.97725-0.84134$

$=0.13591$

Hence,  the probability that the average score of a group of n = 4 people is between 70 and 75=0.13591