Exam 6: The Normal Probability Distribution

Suppose z has a standard normal distribution. Then 85.08% of the possible z-values are smaller than which z-value?

For a normal curve, if the mean is 25 minutes and the standard deviation is 5 minutes, the area to the left of 10 minutes is about 0.50.

Learning Time of Computer Software Narrative The time x a student spends learning a computer software package is normally distributed with a mean of 8 hours and a standard deviation of 1.5 hours. A student is selected at random. -Refer to Learning Time of Computer Software Narrative. What is the probability that the student spends between 6.5 and 8.5 hours learning the software package?

Twenty percent of Canadian men over 30 have high blood pressure. To run an experiment, a researcher needs to identify at least 15 men with high blood pressure. If the researcher examines 100 men over 30, what is the approximate probability he or she finds enough men with high blood pressure to run the experiment?

For any random variable x and constant a, P(x a) = P(x < a) because P(x = a) = 0.

Given that Z is a standard normal random variable, which of the following is the value for P(Z > -1.58)?

Suppose z has a standard normal distribution. Then above which z-value would 16.6% of the possible z-values occur?

Which of the following probability distributions can be used to describe the distribution for a continuous random variable?

If z is a standard normal random variable, what is the value of P(-1.25 z -0.75)?

The relative frequency associated with a particular class in the population is the fraction of measurements in the population falling in that class.

Water Usage Narrative The mayor of the city of Windsor was informed that household water usage is a normally distributed random variable with a mean of 95 litres and a standard deviation of 16 litres per day. -If X is a normal random variable with a mean of 45 and a standard deviation of 8, find the following probabilities: a. P(X 50) b. P(X 32) c. P(37 X 48) d. P(50 X 60) e. P(X = 45)

Canada Revenue Agency Audits Narrative How does Canada Revenue Agency decide on the percentage of income tax returns to audit for each province? Suppose the Agency does it by randomly selecting 50 values from a normal distribution with a mean equal to 1.25% and a standard deviation equal to 0.4%. -Refer to Canada Revenue Agency Audits Narrative. What is the probability that a province will have less than 1% of its income tax returns audited?

High School Graduates IQ's The distribution of IQ scores for high school graduates is normally distributed with = 104 and = 16. -Refer to High School Graduates IQ's paragraph. Find the probability a person chosen at random from this group has an IQ score above 146.

Water Usage Narrative The mayor of the city of Windsor was informed that household water usage is a normally distributed random variable with a mean of 95 litres and a standard deviation of 16 litres per day. -Refer to Water Usage Narrative. Find the probability that a randomly chosen household uses between 75 and 95 litres per day.

The average length of time required to complete a college achievement test was found to equal 75 minutes, with a standard deviation of 15 minutes. When should the test be terminated if you wish to allow sufficient time for 90% of the students to complete the test? (Assume that the time required to complete the test is normally distributed.)