Question

The average number of moves a person makes in his or her lifetime is 12. If the standard deviation is 3.2, find the probability that the mean of a sample of 36 people is less than 10.

Answer 1

Answer:

0.0001

Step-by-step explanation:

The average number of moves a person makes in his or her lifetime is 12.

We want to find the probability that the mean of a sample of 36 people is less than 10, if the standard deviation is 3.2.

We calculate the z-score using the formula:

$z=\frac{ \bar \: X-\mu}{\frac{\sigma}{\sqrt{n}}}$

We substitute the values to get:

$z=\frac{10-12}{\frac{3.2}{\sqrt{36}}}$

We simplify to get;

$z=\frac{ - 2}{\frac{3.2}{6}} = - 3.75$

From the standard normal distribution table we read -3.7 under 5 to obtain the area to the left of -3.75 as 0.0001