http://www.ck12.org Chapter 5. Normal Distribution
Review Questions
- Estimate the standard deviation of the following distribution.
- Thez−table most commonly gives the probabilitiesbelowthe givenz−score, or what are sometimes referred
to asleft tail probabilities. Probabilities above a certainz−score are complementary to those below, so all we
have to do is subtract the table value from 1. To calculate the probabilitiesbetweentwoz−scores, calculate
the left tail probabilities for bothz−scores and subtract the left-most value from the right. Try these using the
table only!!
a.P(z≥− 0. 79 )
b. Use the table to verify the empirical rule value for:P(− 1 ≤z≤ 1 ). Show all work.
c.P(− 1. 56 ≤z≤ 0. 32 ) - Brielle’s statistics class took a quiz and the results were normally distributed with a mean of 85 and a standard
deviation of 7. She wanted to calculate the percentage of the class that got aB(between 80 and 90). She used
her calculator and was puzzled by the result. Here is a screen shot of her calculator.
a. Explain her mistake and the resulting answer on the calculator.
b. Calculate the correct answer.- Which grade is better:A78 on a test whose mean is 72 and standard deviation is 6.5, or an 83 on a test whose
mean is 77 and standard deviation is 8.4. Justify your answer and draw sketches of each distribution. - TeachersAandBhave final exam scores that are approximately normally distributed with the mean for Teacher
Aequal to 72 and the mean for TeacherBis 82. The standard deviation ofA′sscores is 10 and the standard
deviation ofB′sscores is 5.
a. With which teacher is a score of 90 more impressive? Support your answer with appropriate probability
calculations and with a sketch.
b. With which teacher is a score of 60 more discouraging? Again support your answer with appropriate
probability calculations and with a sketch.