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9. An instructor reported that on a test administered to 60 students, the mean was 65 and the standard deviation was 10. Estimate a. The number of grades between 45 and 85. The number of grades above 85. c. What assumption is implicit in these estimates?

Answer 1

here n=60,

mean(ū)=65,

sd(ś)=10

a)X₁₌45; X₂=85

let us consider X_1,X_{2~normal distribution.}

_{we calculate, Z1=(}X_{1-ū)/ś Z2=(}X_2-ū)/ś

_{on substituting values we have, Z1=(45-65)/10=-2}

_{Z2=(85-65)/10=2}

_{from the normal distribution table:}

_{A1=1-0.4772=0.5228(since Z1 is negative) A2=0.4772}

No of students below 45= No of students above 85=

0.5228*60=31.368=31(approximated) 0.4772*60=28.632=29(approximated)

so,p(45<x<85)=60-(31+29)=0

2

b)no of grades above 85=p(x>85)=29[previous calculation]

c)here we have considered that the mean mark of students is normally distributed.