Exam 7: Continuous Probability Distributions

The annual income for a sample of 500 part-time students is normally distributed with a mean income of $30,000 and a standard deviation of $3,000. The income range that separates the top 25% from the lower 75% is __________.

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

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?

Describe the uniform distribution.

What is the area under the normal curve between z = 0.0 and z = 1.79?

A major credit card company has determined that customers charge between $100 and $1100 per month. If the monthly amount charged is uniformly distributed, the standard deviation of the monthly amount charged would be ________.

The total area of a normal probability distribution is _______.

Which of the following is true in a normal distribution?

The mean amount spent by a family of four on food is $500 per month with a standard deviation of $75. Assuming that the food costs are normally distributed, what is the probability that a family spends less than $410 per month?

A large manufacturing firm tests job applicants. Test scores are normally distributed with a mean of 500 and a standard deviation of 50. Management is considering placing a new hire in an upper-level management position if the person scores in the upper sixth percent of the distribution. What is the lowest score a new hire must earn to qualify for a responsible position?

The weight of a bag of corn chips is normally distributed with a mean of 22 ounces and a standard deviation of 0.5 ounces. The probability that a bag of corn chips weighs more than 23 ounces is ____.

The mean of any uniform probability distribution is _________.

What happens to the shape of a binomial distribution as the number of trials increases?

The proportion of the area under a normal curve that is to the left of z = 0.50 is _______.

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

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the distribution's mean?

Two normal distributions are compared. One has a mean of 10 and a standard deviation of 10. The second normal distribution has a mean of 10 and a standard deviation of 2. Which of the following is true?

For the exponential distribution, the mean and standard deviation are equal.

A binomial distribution has 50 trials (n = 50) with a probability of success of 0.50 (π = 0.50). To use the normal distribution to approximate the binomial, what are the mean and standard deviation?

A major credit card company has determined that customers charge between $100 and $1,100 per month. If the average monthly amount charged is uniformly distributed, the percent of monthly changes between $311 and $889 is _______.