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

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=(x-\mu)/(\sigma)`

Using the x values it follows:

`z=(57-62)/(4)=-1.25`

Also,

`z=(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