Exam 7: Continuous Probability Distributions

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?

About ______% of the area under the normal curve is within plus two and minus two standard deviations of the mean.

A study conducted by a local tennis center revealed that 25 percent of its new members have novice level tennis skills. A membership drive in a metropolitan area resulted in 500 new members. What is the mean and standard deviation to apply the normal approximation to the binomial?

The z-scores for X values greater than the mean are negative.

A binomial distribution has 100 trials (n = 100) with a probability of success of 0.25 (π = 0.25). To apply the normal distribution to approximate the binomial, what are the mean and standard deviation?

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 probability that a flight is between 125 and 140 minutes?

Management is considering a bonus system to increase production. One suggestion is to pay a bonus on the highest 5% of production based on past experience. Past records indicate that an average of 4,000 units of a small assembly is produced during a week. The distribution of the weekly production is approximately normally distributed with a standard deviation of 60 units. If the bonus is paid on the upper 5% of production, the bonus will be paid on how many units or more?

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

The formula used to compute the standard deviation is ________.

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 who earned more than $36,000 was ______.

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 probability that a flight is less than 135 minutes?

Consider a standard normal random variable z. What is the value of z if the area to the right of z is 0.2643?

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

Within plus and minus one standard deviation of the mean, the area under any normal curve is about 68%.

The normal distribution can be used to approximate a binomial distribution when nπ is less than 5.