The distribution of exam grades for an introductory psychology class is negative

Question

The distribution of exam grades for an introductory psychology class is negatively skewed with a mean of -71.5 and a standard deviation of = 12·Using the Distributions tool, answer the questions that follow. Standard Normal Distribution Mean = 0.0 Standard Deviation = 1.0 5000 5000 -3 -2 -1 0.000 What is the probability of selecting a random sample of n 9 students with an average exam grade greater than 75 approximate a normal distribution, and By the central limit theorem, the negatively skewed distribution the probability of selecting a random sample of n = 9 students with an average exam grade greater than 75 What is the probability of selecting a random sample of n 36 students with an average exam grade greater than 75? By the central limit theorem, the negatively skewed distribution the probability of selecting a random sample of n-36 students with an average exam grade greater than 75 approximate a normal distribution, and For a sample of n = 36 students, what is the probability that the average exam grade is between 70 and 75?

Explanation / Answer

mean = 71.5
std. dev. = 12

a) n = 9
P(X > 75)
= P(z > (75 - 71.5)/(12/sqrt(9))
= P(z > 0.875)
= 0.1908 (using standard z-table)

b) n = 36
P(X > 75)
= P(z > (75 - 71.5)/(12/sqrt(36))
= P(z > 1.75)
= 0.0401 (using standard z-table)

c) n = 36
P(70 < X < 75)
= P((70 - 71.5)/(12/sqrt(36)) < z < (75 - 71.5)/(12/sqrt(36)))
= P(-0.75 < z < 1.75)
= P(z < 1.75) - P(z < -0.75)
= 0.9599 - 0.2266 (using standard z-table)
= 0.7333

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