I need to find the proportion using mean and s.d.

Question

A movie fan calculated that the mean running time of horror films made in the 1980’s was 90 minutes with a standard deviation of eight minutes. Given that 7,250 horror films were made in the 1980’s how many would you expect to run for: a) Between 66 and 114 minutes? b) Between 74 and 106 minutes?

Answer 1

As you can see from the image above, $99.8\%$ data on a standard distribution fall within $3$ standard deviations of the mean, which is the range for part $(a)$, so the answer part $(a)$ would be $0.998\times7250\approx7236$ movies.

Note: Some people say that $99.7\%$ of the data fall within $3$ standard deviations of the mean; in that case the answer would be $0.997\times7250\approx7228$ movies.

For part $(b)$, you can see from this same image above that $95.4\%$ of the data fall within $2$ standard deviations of the mean, so the answer to part $(b)$ would be $0.954\times7250\approx6917$ movies.