Question

On a test given to 570 students, the mean grade was 80.6% with a standard deviation of 4.4%. Assuming a normal distribution, predict the number of grades:

a.) A grades, over 90%, ?(?????≥90%)

b.) failing grades, less than 60%, ?(?????<60%).

Answer 1

Please don't hesitate to give a "thumbs up" for the answer in case the answer has helped you

The normal distribution parameters are given as:

Mean, Mu = 80.6%
Stdev, Sigma = 4.4%

Formula to standardizie: (X-Mean)/(Stdev)

a. P(grade>=90%) = ?
Lets standardize the distribution using the above formula:
= P(Z> (90%-80.6%)/4.4%)
= P(Z>2.1364)
= 1- P(Z<=2.1364)
= 1- 0.9837
= 0.0163

b. P(X<60%), standardizing:
= P(Z<(60%-80.6%)/4.4%)
= P(Z<-4.682)
= 0.0000