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 relative - frequency distribution as shown here: height (cm) 130 - 144 145 - 159 160 - 174 175 - 189 190 - 204 relative frequency 23% 26% 22% 28% 27% select all that apply. a. 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. b. all of the relative frequencies are different. if they are from a normal distribution, they should all be exactly the same. c. the sum of the relative frequencies is 126%, but it should be 100%, with a small possible round - off error. d. the relative frequencies were recorded as percents instead of counts. e. 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. f. 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.

Explanation:

Step1: Recall properties of relative - frequencies

The sum of all relative frequencies in a distribution must equal 100% (or 1 in decimal form). If the sum is 126% as stated, it is incorrect.

Step2: Analyze normal - distribution characteristics

In a normal distribution, relative frequencies should follow a bell - shaped pattern. The classes should allow for values within the entire range of possible data. If the classes don't allow for values less than 130 cm or greater than 204 cm while assuming a normal distribution of adult male heights, it is a flaw. Also, relative frequencies from a normal distribution should roughly follow a certain pattern and not be wildly different from what is expected.

Answer:

A. 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 126%, but it should be 100%, with a small possible round - off error
D. The relative frequencies were recorded as percents instead of counts
E. 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