Question

A pizza delivery vendor has a goal of delivering all orders within 50 minutes. A sample was taken and found a mean of 40 minutes and a sample standard deviation of 6 minutes.

Assuming the distribution is normal, what percent of the population did not meet the goal of 50 minutes?

Answer 1

A normal distribution is basically a function of standard deviation and mean.

To find the percent of the population that did not meet the goal of 50 minutes, one needs to refer to the normal distribution table available easily anywhere on the internet. The said table is basically an equation for the cumulative probability of a random normal variable across the normal distribution. Since the distribution is normal in this case, the table could be referred.

Find the Z-score of the equation which would be used to find the cumulative probability in the table

Where, X = random variable from the distribution i.e. 50 in this question

= Mean i.e. 40 minutes

= Standard deviation i.e. 6

Therefore Z = (50-40)/6 = ~ 1.66

1.66 needs to be considered to be located in the normal distribution table accordingly and the desired figure comes out to be 0.952 i.e. the probability of meeting the goal is 95.2% which implies the probability or rather, the percent of population not meeting the goal is ( 1 - 0.952 ) i.e. 0.048 / 4.8%