A set of 900 exam scores is normally distributed with a mean = 82 and standard deviation = 5.

Question

A set of 900 exam scores is normally distributed with a mean = 82 and standard deviation = 5.

How many students scored between 77 and 87? Incorrect

How many students scored between 72 and 92? Incorrect

How many students scored between 82 and 87? Incorrect

How many students scored lower than 77? 

Answer 1

Use the z-score table to find the p-value(s) for each problem.

z = (77 - 82)/5 = -5/5 = -1

z = (87 - 82)/5 = 5/5 = 1

P(-1 < z < 1) = 0.8413 - 0.1587 = 0.6826

The probability of students who scored their exam between 77 and 87 is 0.6826.

z = (72 - 82)/5 = -10/5 = -2

z = (92 - 82)/5 = 10/5 = 2

P(-2 < z < 2) = 0.9772 - 0.0228 = 0.9544

The probability of students who scored their exam between 72 and 92 is 0.9544.

z = (82 - 82)/5 = 0/5 = 0

z = (87 - 82)/5 = 5/5 = 1

P(0 < z < 1) = 0.8413 - 0.5000 = 0.3413

The probability of students who scored their exam between 82 and 87 is 0.3413.

z = (77 - 82)/5 = -5/5 = -1

P(z < 1) = 0.1587

The probability of students who scored their exam below 77 is 0.1587.