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=\dfrac{X_1-\mu}{\sigma}=\dfrac{21-18.5}{3.25}=\dfrac{2.5}{3.25}=0.769$$z_2=\dfrac{X_2-\mu}{\sigma}=\dfrac{27-18.5}{3.25}=\dfrac{8.5}{3.25}=2.615$

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

$\begin{gathered} P(21As the proportion is 0.197, the number of values will be:[tex]Y=p\cdot N=0.197\cdot600=118.2\approx118$

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

Answer: 130