Question

BUS DATA

76. Refer to the Lincolnville School District bus data. a. Refer to the maintenance cost variable. The mean maintenance cost for last year is $4,552 with a standard deviation of $2332. Estimate the number of buses with a maintenance cost of more than $6,000. Compare that with the actual number. Create a frequency distribution of maintenance cost. Is the distribution normally distributed? b. Refer to the variable on the number of miles driven since the last maintenance. The mean is 11,121 and the standard deviation is 617 miles. Estimate the number cf buses traveling more than 11,500 miles since the last maintenance. Compare that number with the actual value. Create a frequency distribution of miles since mainte nance cost. Is the distribution normally distributed?

Answer 1

The population mean and standard deviation is,

$\mu=4552\ \ \ \sigma=2332$

The probability that a maintenance cost is greater than $6000 is obtained by first converting the normal distribution to standard normal than the probability can be obtained using the standard normal distribution table,

$P\left ( X>6000 \right )\Rightarrow P\left ( \frac{X-\mu}{\sigma}> \frac{6000-\mu}{\sigma}\right )=P\left ( z>\frac{6000-4552}{2332} \right )=P\left ( z>0.620926 \right )$

$P\left ( z>0.620926 \right )=1-P\left ( z<0.620926 \right )=1-0.732676=0.267324$

For 80 buses, the total buses with maintenanance greater than 6000

$X=80\times 0.267324=21.38593\approx 22$

From the provided bus data with sample size = 80, number of buses with maintenance cost greater than 6000 can be obtain using the function in excel =COUNTIF(B2:B81,">6000")

The count = 17 out of 80 buses

The actual count is 17 while the calculated from distribution is 21

The frquency diagram is obtained in excel using the following steps,

Step 1: Write the data values of Maintenance cost in excel

Step 2: Make Bin column with data value 1000, 2000, .......11000.

Step 2: DATA > Data Analysis > Historam > OK. The screenshot is shown below,

Step 4: Select Input Range: Maintenance column, Bin Range: Bin column. The screenshot is shown below,

The output is,

Step 5: Select the Bin and frequency column then INSERT > Recommended Charts > All Charts > Column > OK. The screenshot is shown below,

The plot is normally distributed

Part (b) is same, Comment me if got stuck