Question

1000 students took an examination in Statistics and Probability. The mean score obtained is 70 and the

standard deviation is 3. Assuming that the data are normally distributed, find the area and probability of

students who obtained a score of:

a. at least 83

b. mean to 95

c. at most 75

Answer 1

a. $P(X>83)=P(Z>\frac{83-70}{3})=P(Z>4.33)=1-P(Z<4.33)=7.5*10^{-6}.$

$N=1000*7.5*10^{-6}=0.$

b. $P(70<X<95)=P(0<Z<\frac{95-70}{3})=P(0<Z<8.33)=$

$=P(Z<8.33)-P(Z<0)=0.5.$

$N=1000*0.5=500.$

c. $P(X<75)=P(Z<\frac{75-70}{3})=P(Z<0.67)=0.7486.$

$N=1000*0.7486=749.$