Exam 7: Continuous Probability Distributions

A national manufacturer of unattached garages discovered that the distribution of the time for two construction workers to erect the Red Barn model is normally distributed with a mean of 32 hours and a standard deviation of 2 hours. What percent of the garages take between 32 and 34 hours to erect?

For a standard normal distribution, what is the probability that z is greater than 1.75?

The shape of any uniform probability distribution is ____________.

A study of a company's practice regarding the payment of invoices revealed that an invoice was paid an average of 20 days after it was received. The standard deviation equaled five days. Assuming that the distribution is normal, what percent of the invoices were paid within 15 days of receipt?

Two business major students, in different sections of an economics class, were comparing test scores. The following shows the sections' mean and standard deviation. The student in section 1 scored 84. The student's z score would be _________.

From past history, the scores on a statistics test are normally distributed with a mean score of 70 and a standard deviation of 5. To earn a "C" on the test, a student must be in the top 25% of the class. A student would need to score at least ______ to receive a "C" grade.

A sample of 500 part-time students revealed that their annual incomes were normally distributed with a mean income of $30,000 and a standard deviation of $3,000. The number of students that earned between $27,000 and $33,000 is _____.

In a uniform distribution, with a minimum, a, and maximum, b, the probability that the random variable, x, is between a and b is ___________.

For a uniformly distributed random variable, x, P(x) is constant.

What is a normal distribution with a mean of 0 and a standard deviation of 1 called?

For any uniform probability distribution, the mean and standard deviation can be computed based on the maximum and minimum values of the random variable.

A group of normal distributions can have equal arithmetic means but different standard deviations.

The expected value of a uniform distribution is computed using the formula _________.

The standard normal distribution is a special normal distribution with a mean of 0 and a standard deviation of 1.

Suppose a tire manufacturer wants to set a mileage guarantee on its new XB 70 tire. Tests revealed that the tire's mileage is normally distributed with a mean of 47,900 miles and a standard deviation of 2,050 miles. The manufacturer wants to set the guaranteed mileage so that no more than 5% of the tires will have to be replaced. What guaranteed mileage should the manufacturer announce?

The mean of any uniform probability distribution is _________.

The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. Assuming a normal distribution, what test score separates the top 25% of the students from the lower 75% of students?

The average score of 100 students taking a statistics final was 70, with a standard deviation of 7. Assuming a normal distribution, what test score separates the top 5% of the students from the lower 95% of the students?

The proportion of the area under a normal curve that is to the right of z = -1.21 is _______.

The weekly incomes of a large group of executives are normally distributed with a mean of $2,000 and a standard deviation of $100. What is the z-score for an income of $2,100?