Suppose that the average on the math final is 62%. a. What can you say about the

Question

Suppose that the average on the math final is 62%.

a. What can you say about the probability that any given student's score will exceed 85%?

b. Suppose that we know also that the variance of these data in 142. Can you obtain a better estimate, without using the central limit theorem, for the probability that the student's score will exceed 85%? What is the estimate you get with the central limit theorem?

c. Now also suppose that a math class has 16 students enrolled in it. Give two estimates for the probability that the average in that class is greater than 70%?

Explanation / Answer

Suppose that the average on the math final is 62%.

a. What can you say about the probability that any given student's score will exceed 85%?

I would say that more than half can exceed 85% of the score because if mean is 62% that means that at least 50% of the students has a score of 62%

b. Suppose that we know also that the variance of these data in 142. Can you obtain a better estimate, without using the central limit theorem, for the probability that the student's score will exceed 85%? What is the estimate you get with the central limit theorem?

P( z > 85 - 62 / srqt 142 )

P( z >1.93 ) = 0.0268

c. Now also suppose that a math class has 16 students enrolled in it. Give two estimates for the probability that the average in that class is greater than 70%?

P( z > 0.70 - 0.62 / srqt ( 0.62*0.38 / 16 ) )

P( z > 0.66) = 0.2546

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