Question 328042: 2. In 2000, as reported by ACT Research Service, the mean ACT Math score was μ=20.7. If ACT Math scores are normally distributed with σ = 5, answer the following questions.
a) What is the probability that a randomly selected student has an ACT Math score less than18?
b) What is the probability that a random sample of 10 ACT test takers had a mean ACT Math score less than 18?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In 2000, as reported by ACT Research Service, the mean ACT Math score was μ=20.7. If ACT Math scores are normally distributed with σ = 5, answer the following questions.
a) What is the probability that a randomly selected student has an ACT Math score less than 18?
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z(18) = (18-20.7)/5 = -0.54
P(x < 18) = P(z < -0.54) = 0.2946
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b) What is the probability that a random sample of 10 ACT test takers had a mean ACT Math score less than 18?
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z(18) = (18-20.7)/[5/sqrt(10)] = -1.7076 = 0.0439
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Cheers,
Stan H.
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