Question

The mean stay of a car on a lot before being sold is 21 days, with a standard deviation of 3 days. The lengthsof stay are normally distributed. What percent of the cars are sold after having been on the lot between 18and 24 days?A 5%B 34%C 68%D 95%

Answer 1

Given:

Mean=21.

Standard deviation, SD=3.

The percentage of cars sold between 18 and 24 days is to be found.

So, upper value=24.

Lower value=18

$1\text{ S.D=}\frac{upper\text{ value-lower value}}{\text{Total number of standard deviations}}$

Now, find total number of standarde deviations from above equation.

$\begin{gathered} \text{Total number of standard deviations=}\frac{upper\text{ value-lower value}}{1\text{ S.D.}} \\ =\frac{24-18}{3} \\ =2 \end{gathered}$

A total of two standard deviations implies that there is one standard deviation on either side of the mean.

Generally, 68% of the values are within one standard deviation of the mean.

Hence, option C is correct.