Question

Pizza delivery times at Pizza Time are normally distributed with a mean time of 27 minutes and a standard deviation of 3 minutes. Approximately what percent of pizzas are delivered between 24 and 30 minutes? What percent is above 30 minutes? What percent is below 24 minutes

Answer 1

= 27*3 = 81 And 24*30 = 720.

Now, 720 + 81 = 801.

Now, 30*24 = 720.

So, 801-720 = 81.

Answer 2

Answer: 24 minutes.

Given :

Normal distribution, mean μ = 27 minutes, standard deviation σ=3 minutes

Percentage of pizzas that are delivered between 24 minutes and 30 minutes

                       24 minutes  = 27-3 = μ-σ

                        30 minutes = 27+3 = μ+σ

So the percentage of area that covers from μ-σ to μ+σ is 68.26%

Thus approximately, 68% of pizzas are delivered between 24 minutes and 30 minutes.

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Percentage of pizzas that are delivered above 30 minutes

                          $Z = \frac{(X- \mu)} {\sigma}$

X = 30 minutes

                 $Z = \frac { (30-27) }{ 3 } ={ \frac { 3 }{ 3 }  } =1$

If Z = 1, it means one standard deviation above the mean

As we know that one standard deviation above and below the mean covers about 68% of the area,  so one standard deviation above the mean implies the 50% below the mean plus the 34% (which is half of 68) above the mean gives us 84%.

So  approximately 84% of pizzas are delivered above 30 minutes.

       Percentage of pizzas that are delivered below 24 minutes

                           $Z=\frac{(X- \mu)}{\sigma}$

X = 24 minutes

                    $Z=\frac{(24-27)}{3}=\frac{-3}{3} = -1$

If Z = 1, it means one standard deviation above the mean

As we know that one standard deviation above and below the mean covers about 68% of the area,  so one standard deviation above the mean implies the 50% below the mean minus the 34% (which is half of 68) above the mean gives us 16%.

So  approximately 16% of pizzas are delivered below 24 minutes.