Chapter 11.10, Problem 34PPSE

Solution

To find: To find the percent of flights that are expected to have 340 to 420 pieces of checked luggage.

The percent of flights that are expected to have 340 to 420 pieces of checked luggage is 95%

Given information:

Given, for a daily airline flight between two cities, the number of pieces of checked luggage has a mean of 380 and a standard deviation of 20.

Calculation:

One standard deviation below and above the mean are:

  $\begin{array}{l}380-20=360\\ 380+20=400\end{array}$

Two standard deviation below and above the mean are:

  $\begin{array}{l}380-2\left(20\right)=340\\ 380+2\left(20\right)=420\end{array}$

Three standard deviation below and above the mean are:

  $\begin{array}{l}380-3\left(20\right)=320\\ 380+3\left(20\right)=440\end{array}$

In a normal distribution, the data is distributed equally i.e., 50% on either side of the mean.

The data within the first standard deviation contains 34% of data on each side.

The data between the first standard deviation and second standard deviation contains 13.5% of data on each side.

The data between the second standard deviation and third standard deviation contains 2.35% of data on each side.

Here, 340 is the second standard deviation on the left of mean and 420 is the second standard deviation on the right of mean.

Hence the percent of data between 340 and 420 is given by:

  $\begin{array}{l}p\approx 13.5+34+34+13.5\\ p\approx 95\%\end{array}$

Conclusion:

The percent of flights that are expected to have 340 to 420 pieces of checked luggage is 95%