Question

The final marks for the Wednesday class in Statistics 101 are ready to be posted. The class average is 80%, with a standard deviation of 5. The distribution of grades is approximately bell-shaped. (Round the final answers to 2 decimal places.) a. What percentage of the grades are above 85? Percentage of grades % b. What percentage of the grades are below 75? Percentage of grades % c. What percentage of the grades are between 70 and 85? Percentage of grades % d. What percentage of the grades are between 70 and 90? Percentage of grades % e. What percentage of the grades are between 70 and 95? Percentage of grades % f. What percentage of the grades are less than 65 or more than 85? Percentage of grades %

Statistics

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	80
std deviation   =σ=	5

percentage of the grades are above 85 :

probability =P(X>85)=P(Z>(85-80)/5)=P(Z>1)=1-P(Z<1)=1-0.8413=0.1587~ 15.87 %

b) percentage of the grades are below 75 :

probability =P(X<75)=(Z<(75-80)/5)=P(Z<-1)=0.1587~ 15.87%

c)

probability =P(70<X<85)=P((70-80)/5)<Z<(85-80)/5)=P(-2<Z<1)=0.8413-0.0228=0.8185~ 81.85%

d)

probability =P(70<X<90)=P((70-80)/5)<Z<(90-80)/5)=P(-2<Z<2)=0.9772-0.0228=0.9544~ 95.44 %

e)

probability =P(70<X<95)=P((70-80)/5)<Z<(95-80)/5)=P(-2<Z<3)=0.9987-0.0228=0.9759~ 97.59% f)

probability =1-P(65<X<95)=1-P((65-80)/5)<Z<(95-80)/5)=1-P(-3<Z<3)=1-(0.9987-0.0013)=0.0026~ 0.26 %