Question

The measurement of the height of 600 students of a college is normally distributed with a mean of

Answer 1

Answer: Second Option

$P(180$

We know that the mean is:

$\mu=175$

and the standard deviation is:

$\sigma=5$

We are looking at the percentage of students between 180 centimeters and 185 centimeters in height.

This is:

$P(180$

We calculate the Z-score using the formula:

$Z=\frac{X-\mu}{\sigma}$

For $X=180$

$Z_{180}=\frac{180-175}{5}$

$Z_{180}=1$

For $X=185$

$Z_{185}=\frac{185-175}{5}$

$Z_{185}=2$

Then we look at the normal table

$P(1$

$P(1$

$P(1$

$P(1$

$P(180$

Note: You can get the same conclusion using the empirical rule

Look at the attached image for $\mu+ 1\sigma$