Question

a. Find Z score (Z_a) when a=0.75. In other words, find Z_0.75 Draw a visual display.

Through data collection and analysis done by the environmental protection agency, they estimate that 2019 automobile models have a fuel economy with a mean of 25.2 miles per gallon and a standard deviation of 5.8 miles per gallon.

b. Uses your rounded Z_a from above to determine the lowest and highest fuel economy for the middlemost 75% of the distribution. Verify with invnorm function on calculator.

Answer 1

Solution: a) To find the value of Z(0.75), we can use the standard normal table to find the Z(0.75).

b. To find the middlemost 75% of the z-values, we first need to find the z-value corresponding to area = 0.25/2=0.125. Using the standard normal table, we have:

Now to find the upper value of the middle 75%, we need to find the z-value corresponding to area = 0.75+ 0.125=0.875. Using the standard normal table, we have:

Therefore, the middle z-values that cover the middlemost 75% of data are -1.150 and 1.150

The calculator functions are:

invNORM(0.125,0,1) and invNORM(0.875,0,1)