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?

0.9545

Step-by-step 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
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