Question

heights of adult males are known to have a normal distribution. a researcher claims to have randomly selected adult males and measured their heights with the resulting frequency distribution as shown here. identify two major flaws with these results.
relative
height (cm) frequency
130 - 144 23%
145 - 159 26%
160 - 174 21%
175 - 189 28%
190 - 204 29%
select all that apply.
a. all of the relative frequencies appear to be roughly the same. if they are from a normal distribution, they should start low, reach a maximum, and then decrease.
b. the classes do not allow for the possibility that an adult male could be less than 130 cm tall or greater than 204 cm tall.
c. the sum of the relative frequencies is 127%, but it should be 100%, with a small possible round - off error.
d. the relative frequencies were recorded as percents instead of counts.
e. the classes do not allow for the possibility that an adult male could be between 144 cm and 145 cm tall, or between 159 cm and 160 cm tall, and so on.
f. all of the relative frequencies are different. if they are from a normal distribution, they should all be exactly the same.

Explanation:

• In a normal distribution, relative - frequencies should follow a bell - shaped pattern (start low, peak, then decrease), not be roughly equal as in option A.
• The sum of relative frequencies in a proper distribution should be close to 100% (with a small round - off error), not 127% as in option C.
• The class intervals have gaps (e.g., no values between 144 and 145 cm are accounted for) as in option E.
• The classes also have a limited range and don't account for values outside 130 - 204 cm as in option B.

Answer:

A. All of the relative frequencies appear to be roughly the same. If they are from a normal distribution, they should start low, reach a maximum, and then decrease.
B. The classes do not allow for the possibility that an adult male could be less than 130 cm tall or greater than 204 cm tall.
C. The sum of the relative frequencies is 127%, but it should be 100%, with a small possible round - off error.
E. The classes do not allow for the possibility that an adult male could be between 144 cm and 145 cm tall, or between 159 cm and 160 cm tall, and so on.