Some students paid a private tutor to 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 them improve their results, what is the likelihood that the change in the sample mean score is less than 10 points?

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

Step-by-step explanation:

Given : Mean :

Standard deviation :

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 :

For x = 10

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

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 .