Question

A study uses a sample of 200 college students to learn about the number of hours they studied for their final exams. The mean number of hours was 136 and the standard deviation was 14 hours. If this data falls under a normal distribution or bell curve, which of the following statements is NOT true?

The number of students that studied 122 or fewer hours was about 32.

The number of students that studied 150 or fewer hours was about 168.

The majority of students studied between 122 and 150 hours.

No one studied less than 108 hours.

Answer 1

`\displaystyle\mathbb P(X\le122)=\mathbb P\left((X-136)/(14)\le(122-136)/(14)\right)=\mathbb P(Z\le-1)\approx0.1587`
which means
`0.1587*200\approx32` studied 122 or fewer hours.


`\displaystyle\mathbb P(X\le150)=\mathbb P\left((X-136)/(14)\le(150-136)/(14)\right)=\mathbb P(Z\le1)\approx0.8413`
which means
`0.8413*200\approx168` studied 150 or fewer hours.

So, neither of the first two are false.

Depending on your definition of "majority", you could also eliminate the third option. From the above calculations, you know that students that studied between 122 and 150 hours fall within 1 standard deviation of the mean, which corresponds to approximately 65% of the student population. "Majority" is often taken to mean "more than 50%", so this is also true.

This leaves us with the last option. For fun, let's compute that probability.

`\displaystyle\mathbb P(X<108)=\mathbb P\left((X-136)/(14)<(108-136)/(14)\right)=\mathbb P(Z<-2)\approx0.0228`
which means
`0.0228*200\approx5` students studied less than 108 hours.

Answer 2

No one Studied less than 108 hours

Explanation:

This is the answer because there were about 5 people that did study less than 108 hours! Hope this makes it easier to read