Suppose a review of 40 student grades in a statistics course section revealed th

Question

Suppose a review of 40 student grades in a statistics course section revealed that student grades were normally distributed with a mean of 70 and a standard deviation of 10.

a) Determine the grade that is 0.5 standard deviations above the mean.

b) What is the probability that a student received a grade between 70 (the mean) and the grade obtained in a)?

c) Determine the grade that is 1 standard deviation above the mean.

d) What is the probability that a student receives a grade that is between the grade in a) and the grade in c)?

Explanation / Answer

a) Grade:70+0.5*10=75

b) Xbar=70, s=10. Compute z scores corresponding to Xi=70 and 75.

Z1=(Xi-Xbar)/s=(70-70)/10=0 and Z2=(75-70)/10=0.5

P(70<X<75)=0.1915-0.0000=0.1915 (scores are on same side, subtract smaller from higher area).

c) Grade:70+1*10=70

d) Z1=(75-70)/10=0.5 Z2=(70-70)/10=0

P(70<X<75)=0.1915-0.0000=0.1915

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