Question

A normally distributed data set of 600 values has a mean of18.5 and a standard deviation of 3.25.Which is closest to the expected number of values in thedata set that lie between 21 and 27?

Answer 1

We have a sample of 600 values.

They belong to a population that have a mean of 18.5 and a standard deviation of 3.25.

We have to calculate the expected proportion of those values that will lie between 21 and 27.

We can do it calculating the z-scores for each extreme of the interval [21, 27]:

`z_1=(X_1-\mu)/(\sigma)=(21-18.5)/(3.25)=(2.5)/(3.25)=0.769`
`z_2=(X_2-\mu)/(\sigma)=(27-18.5)/(3.25)=(8.5)/(3.25)=2.615`

Then, we can approximate the proportion as the probability of this interval:

From the options, 130 is the closest number to our estimation.

Answer: 130