Question

The heights (in inches) of men listed in the accompanying table have a distribution that is approximately normal, so it appears that those heights are from a normally distributed population. Complete parts (a) through (c). Click the icon to view the data set. X Х

a. If 5 inches is subtracted from each height, are the new heights also normally distributed?
A) YES
B) NO
b. If each height is converted from inches to centimeters, are the heights in centimeters also normally distributed?
A) YES
B) NO
c. Are the logarithms of normally distributed heights also normally distributed?
A) YES
B) NO

Answer 1

a. The new heights will still follow a normal distribution. b. The heights in centimeters will still follow a normal distribution. c. The logarithms of normally distributed heights will also follow a normal distribution.

Step-by-step explanation:

a. If 5 inches is subtracted from each height, the new heights will still follow a normal distribution. This is because subtracting a constant value from a normally distributed variable does not change the shape of the distribution, only the mean and the location of the values.

b. If each height is converted from inches to centimeters, the heights in centimeters will still follow a normal distribution. This is because converting the units of measurement does not change the underlying distribution.

c. The logarithms of normally distributed heights will also follow a normal distribution. This is a property of logarithms; applying a logarithm to a normally distributed variable will result in a new variable that is also normally distributed.