What is the probability thatWhat is the probability thatGiven a normal distribut

Question

What is the probability thatWhat is the probability thatGiven a normal distribution with =100 and =25 and given you select a sample of

n=4, complete parts (a) through (d).

a. What is the probability that r X is less than 93?

b. What is the probability that X is between 93 and 93.5? C. What is the probability that X is above 101.8? D.There is a 66% chance that X is above what value?

c. What is the probability that X overbar is above 101.2?

d. There is a 67% chance that X overbar is above what value?

Explanation / Answer

Answer to the question

Mu = 100

Stdev = 25

n = 4

a. P(X<93) = P(Z< (93-100) /(25/sqrt(4)) = P(Z< -.56) = .2877

b. P(93<X<93.5) = P(-.56<Z< -.52) = .3015 - .2877 = .0138

c. P(X>101.2) = P(Z> 101.2 - 100 /(25/sqrt(4)) = P(Z>.096) = 1-.5398 = .4602

d. P(X>c) = .67, c = ?

(c-100)/(25/sqrt(4)) = -.44

c = 100-.44*25/sqrt(4) = 94.5

So, above 94.5 there is a 66% chance

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