X= average test grades= 72 = standard deviation= 10 20% = have a passing grade (

Question

X= average test grades= 72
= standard deviation= 10
20% = have a passing grade
(a) what is the numerical score of people getting an A?
(b) Choose 5, what is the chance of at most 4 of them will get an A?
(c) We know someone did not get an A. what is the chance the score was less than 60?
X= average test grades= 72
= standard deviation= 10
20% = have a passing grade
(a) what is the numerical score of people getting an A?
(b) Choose 5, what is the chance of at most 4 of them will get an A?
(c) We know someone did not get an A. what is the chance the score was less than 60?
X= average test grades= 72
= standard deviation= 10
20% = have a passing grade
(a) what is the numerical score of people getting an A?
(b) Choose 5, what is the chance of at most 4 of them will get an A?
(c) We know someone did not get an A. what is the chance the score was less than 60?

Explanation / Answer

a) P(X > x) = 0.2

or, P((X - mean)/SD > (x - 72)/10) = 0.2

or, P(Z > (x - 72)/10) = 0.2

or, 1 - P(Z < (x - 72)/10) = 0.2

or, P(Z < (x - 72)/10) = 0.8

or, (x - 72)/10 = 0.84

or, x = 0.84 * 10 + 72

or, x = 80.4

b) P(X < 4 ) = 1- P(X > 4)

                    = 1 - P(X = 5)

                = 1 - (5C5 * (0.2)^5 * (0.8)^0)

= 1 - 0.00032

= 0.99968

c) P(X < 60) = P((X - mean)/sd < (60 - mean)/sd)

   = P(Z < (60 - 72)/10)

= P(Z < -1.2)

= 0.1151

required probability = 0.1151/0.8 = 0.14

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