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?

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JeanaShupp JeanaShupp · Answer 1 · 2019-08-08T06:40:34+02:00

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

Step-by-step explanation:

Given : Mean : [tex]\mu=17\text{ points}[/tex]

Standard deviation : [tex]\sigma= 67\text{ points}[/tex]

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 : [tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

For x = 10

[tex]z=\dfrac{10-17}{\dfrac{67}{\sqrt{100}}}\approx-1.045[/tex]

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

[tex]P(X<10)=P(z<-1.045)=0.1480115[/tex]

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 .