A study of stress on among the students in a college campus shows that the stres

Question

A study of stress on among the students in a college campus shows that the stress scores follow a Uniform distribution with the lowest stress score equal to 1 and the highest equal to 5. [Hint: you may use the Central Limit Theorem]:

(a) The probability that the average stress score for the 75 students is less than 2.

(b) The 90th percentile for the average stress score for the 75 students.

(c) The probability that the total of the 75 stress scores is less than 200.

(d) The 90th percentile for the total stress score for the 75 students.

Explanation / Answer

a. P(X<2) = (2-1)/(5-1) = ,25

b, P(X=x) = .90, x-1/5-1 = .9, x = 4.6 is the score at 90percentile

c. P(X<200) or P(X<200/75 per person) = (200/75) - 1/5-1 = .167

d, P(90ther total score ) = 4.6*75 = 345

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