6. The PRAXIS is a standardized test that all teachers are required to pass befo

Question

6. The PRAXIS is a standardized test that all teachers are required to pass before earning their teaching certificate. Many changes have been made to the PRAXIS over the years, however a few things have remained consistent; the average score by people attempting the test has remained at 605 (out of 1000), the standard deviation is approximately 115, and the distribution of scores is approximately normal each year the test is administered.

(a) What is the probability that a randomly chosen test taker will have a PRAXIS score above 700?

(b) Would it be surprising if someone scored below a 500 on the test? Why or why not?

(c) What are the mean and the standard deviation of the sampling distribution of the average PRAXIS scores for a simple random sample of 16 people?

(d) What is the probability that the average PRAXIS score for a simple random sample of 16 people will be above 700? Show work.

Explanation / Answer

mean = 605 , s = 115

a)

P(x >700)

z = ( x -mean) / (s)

= ( 700 - 605) / 115

= 0.8261

Now, we need to find P(Z > 0.8261)

P(X>700) = P(Z > 0.8261) = 0.2044

b)

P(x <500)

z = ( x -mean) / (s)

= ( 500 - 605) / ( 115 )

= -0.913

Now, we need to find P(Z < -0.913)

P(X<500) = P(Z < -0.913) = 0.1806

c)

for n = 16

mean = 605 and std.dev. = 115/sqrt(16) = 28.75

d)

P(x >700)

z = ( x -mean) / (s/sqrt(n))

= ( 700 - 605) / 28.75

= 3.304

Now, we need to find P(Z > 3.304)

P(X>700) = P(Z > 3.304) = 0.0005

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