Find the indicated probability and interpret the result.

From $1975$ through $2020,$ the mean annual gain of the Dow Jones Industrial Average was $651.$ A random sample of $32$ years is selected from this population. What is the probability that the mean gain for the sample was between $500$ and $800?$ Assume $=1539.$

The probability is

$($Round to four decimal places as needed.$)$

Interpret the result. Select the correct choice and fill in the answer box to complete your choice.

$($Round to two decimal places as needed.$)$

A$.$ About $\%$ of samples of $32$ years will have an annual mean gain between $500$ and $800.$

B$.$ About $\%$ of samples of $46$ years will have an annual mean gain between $500$ and $800.$

C$.$ About $\%$ of samples of $32$ years will have an annual mean gain between $500$ and $651.$

D$.$ About $\%$ of samples of $32$ years will have an annual mean gain between $651$ and $800.$