Question

Suppose you read that the average height of a class of 43 ​eighth-graders is 50 inches with a standard deviation of 40 inches. Is this​ likely? Explain.

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Part 1
Choose the correct answer below.
A.
This is not likely because a mean of 50 and a standard deviation of 40 would imply that about​ 5% of the heights differ from the mean by more than 80 ​, which is impossible.
B.
This is not likely because heights are usually not approximated by the normal distribution.
C.
This is likely because the heights are often accurately approximated by the normal distribution.
D.
This is likely because a mean height of 50 inches is a very plausible height for an​ eighth-grader

Answer 1

The correct answer is option A) This is not likely because a mean of 50 and a standard deviation of 40 would imply that about​ 5% of the heights differ from the mean by more than 80 ​, which is impossible.

Step-by-step explanation:

The question asks whether the reported average height of 50 inches with a standard deviation of 40 inches for a class of 43 eighth-graders is likely. The correct answer here would be A: This is not likely because a mean of 50 and a standard deviation of 40 would imply that about 5% of the heights differ from the mean by more than 80 inches, which is nearly double the mean height and is highly improbable especially considering the relatively young age of eighth-graders for whom heights typically range much more narrowly.

Height data generally follow a normal distribution and, in the case of eighth-graders, would not show such extreme variability. A standard deviation that is almost as large as the mean suggests that the resulting distribution would be very wide, leading to heights that are not physically plausible, such as extremely short or extremely tall students, which would be extremely rare, if even possible, in a typical population of eighth-graders.