Question

Some students paid a private tutor to help them improve their results on a certain mathematical test. These students had a mean change in score of plus17 ​points, with a standard deviation of 67 points. In a random sample of 100 students who pay a private tutor to help them improve their​ results, what is the likelihood that the change in the sample mean score is less than 10​ points?

Answer 1

Answer: Tt is unlikely to have change in the sample mean score is less than 10​ points .

Step-by-step explanation:

Given : Mean : $\mu=17\text{ points}$

Standard deviation : $\sigma= 67\text{ points}$

Sample size : n= 100

We assume that the change in students scores are normally distributed.

Let X be the random variable that represents the change in students scores .

Z score : $z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

For x = 10

$z=\dfrac{10-17}{\dfrac{67}{\sqrt{100}}}\approx-1.045$

By using the standard normal distribution table , the probability  that the change in the sample mean score is less than 10​ points :-

$P(X$

Since the calculated probability is less than 0.5.

So , we say that it is unlikely to have change in the sample mean score is less than 10​ points .