Question

Suppose a normal distribution has a mean of 62 and a standard deviation of4. What is the probability that a data value is between 57 and 65? Round youranswer to the nearest tenth of a percent.

Answer 1

SOLUTION

From the given data the mean is 62 and standard deviation is 4

It is required to find the probability that a data value is between 57 and 62

That is:

$P(57\lt x\lt65)$

The z scores is calculated using:

$z=\frac{x-\mu}{\sigma}$

Using the x values it follows:

$z=\frac{57-62}{4}=-1.25$

Also,

$z=\frac{65-62}{4}=0.75$

Thus the required probability is:

$P(-1.25The proability is:[tex]P(-1.25This can be expressed as percentage as:[tex]P(-1.25\lt z\lt0.75)=66.8\%$

Therefore the correct option is C