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Chapter 5: Q63SE (page 323)

Improving SAT scores. Refer to the Chance(Winter2001) examination of Scholastic Assessment Test (SAT)scores of students who pay a private tutor to help them improve their results, Exercise 2.88 (p. 113). On the SAT鈥擬athematics test, these students had a mean score change of +19 points, with a standard deviation of 65 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 sample mean score change is less than 10 points?

Short Answer

Expert verified

The likelihood that the sample means score change is less than 10 points is 0.0838.

Step by step solution

01

Given information

Referring to exercise 2.88 (p.113), there is a study about 100 students who pay a private tutor to help them improve their results. The students had a mean score of 19 and a standard deviation of 65 points.

02

Determine the likelihood

Let鈥檚 consider the sample mean of 渭x炉=19.

And the sample standard deviation of

蟽x炉=蟽n=65100=6.5

So, the likelihood that the sample mean score change is less than 10 points is,

PrX炉<10=PrX炉-渭x炉蟽x炉<10-196.5=Prz<-1.38=0.0838

Therefore, the likelihood is 0.0838.

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