Question

Randy's average grade is 89 with a standard deviation of 3. His grades follow a normal distribution.

6a. What is the probability that Randy will earn between an 83 and a 95 in a math class?

Answer 1

0.9545

Explanation:

To calculate the probability, we need to get the standard score or z-score of each of the scores.

Mathematically;

z-score = (x-mean)/SD

mean = 89 and SD(standard deviation) = 3

for 83, the z-score = (83-89)/3 = -6/3 = -2

for 95, the z-score = (95-89)/3 = 6/3 = 2

The probability we are to calculate has the following range;

P(-2<z<2)

we use the standard score table to estimate this;

= P(z<2) - P(z<-2)

P(z<2) = 0.97725

P(z<-2) = 0.02275

Plugging these values into the equation, we have ;

P(-2<z<2) = 0.97725 - 0.02275 = 0.9545