The scores of 12th-grade students on the national assessment of educational progress year 2000 mathematics test have a distribution that is approximately normal with mean of 300 and standard deviation of 35.

a. choose one 12th-grader at random. what is the probability that his or her score is higher than 300? higher than 335?

b. now choose an srs of four 12th-graders. what is the probability that their mean score is higher than 300? higher than 335?

Question

Mathematics

Ishaan

10 December, 07:53

The scores of 12th-grade students on the national assessment of educational progress year 2000 mathematics test have a distribution that is approximately normal with mean of 300 and standard deviation of 35.

a. choose one 12th-grader at random. what is the probability that his or her score is higher than 300? higher than 335?

b. now choose an srs of four 12th-graders. what is the probability that their mean score is higher than 300? higher than 335?

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Answers (1)

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Eugene · Answer 1

Z-score is given by:

z = (x-μ) / σ

thus:

a]

i) P (x>300)

z = (300-300) / 35=0

P (x>300) = P (z=0) = 0.5

ii) P (x>335)

z = (335-300) / 35

z=1

P (x>35) = P (z=1) = 0.1587

b] Since we are choosing from the random sample of 4, then first we shall have:

σ/√n

=35/√4=17.5

thus

i] P (x>300)

z = (300-300) / 17.5=0

thus:

P (x>300) = P (z=0) = 0.5

ii] P (x>335)

z = (335-300) / 17.5=2

Thus:

P (x>335) = P (z=2) = 0.9772