# Answer on Statistics and Probability Question for Dan

Question #3870

A standard test given to a large number of student had a mean of 74 with a standard deviation of 8. <br>Find the percentage of students who scored <br>a. between 72 and 80 <br>b. between 68 and 76 <br>c. more than 76

Expert's answer

a. P(72<X<80) = Ф(3/4) + Ф(1/4) = 0.2734 + 0.0987 = 0.3721

ANSWER:

37.2%

b.& P(68<X<76) = Ф(1/4) + Ф(3/4) = 0.0987 + 0.2734 =

0.3721

ANSWER: 37.2%

c. P(X>76) = 1 - P(X<76) = 1 - Ф(1/4) =

0.9013

ANSWER: 90.1%

ANSWER:

37.2%

b.& P(68<X<76) = Ф(1/4) + Ф(3/4) = 0.0987 + 0.2734 =

0.3721

ANSWER: 37.2%

c. P(X>76) = 1 - P(X<76) = 1 - Ф(1/4) =

0.9013

ANSWER: 90.1%

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