Question

The mean grade in this class last semester was 78.3, and the variance was 49 . The distribution of grades was unimodal and symmetrical. Using this information determine the probability that “Joe”, a random student you know nothing about, other than the fact that they are taking this class next semester will receive a grade that is:
Above 90
Between 85 and 95
Between 80 and 90
Lower than 65
Lower than 65 OR above 90


My question is how do you approach this question would i have to do something along these lines?

90-78.3/49?

Answer 1

Z = (score-mean)/SD

SD = √variance

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions/probabilities related to the Z scores.

Either-or probabilities are found by adding the individual probabilities.