Question Help * One college class had a total of 90 students. The average score

Question

Question Help * One college class had a total of 90 students. The average score for the cdass on the last exam was 84 5 with a standard deviation of 55. A random sample of 32 students was selected a. Calculate the standard error of the mean b. What is the probability that the sample mean will be less than 86? c.What is the probability that the sample mean wil be more than 85 d. What is the probability that the sample mean will be between 83.5 and 855 a. The standard error of the mean is Round to two decimal places as needed) b. The probability that the sample mean will be less than 86 is (Round to four decimal places as needed) c. The probability that the sample mean will be more than 85 is (Round to four decimal places as needed) d, The probability that the sample mean will be between 83 5 and 85 5 is? (Round to four decimal places as needed)

Explanation / Answer

Solution :

Given that mean ? = 84.5 , standard deviation ? = 5.5 , n = 32

a. standard error ?x = ?/sqrt(n)

= 5.5/sqrt(32)

= 0.97

b. P(x < 86) = P((x - ?)/?x < (86 - 84.5)/0.97)

= P(Z < 1.5464)

= 0.9394

c. P(x > 85) = P((x - ?)/?x > (85 - 84.5)/0.97)

= P(Z > 0.5155)

= 0.3015

d. P(83.5 < x < 85.5) = P((x - ?)/?x < Z < (x - ?)/?x)

= P((83.5 - 84.5)/0.97 < Z < (85.5 - 84.5)/0.97)

= P(-1.0309 < Z < 1.0309)

= 0.6970

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