Exam 6: Introduction to Continuous Probability Distributions

For a standardized normal distribution, calculate P(z ≥ 0.85).

It is assumed that the time customers spend in a record store is uniformly distributed between 3 and 12 minutes. Based on this information, what is the probability that a customer will be exactly 7.50 minutes in the record store?

Employees at a large computer company earn sick leave in one-minute increments depending on how many hours per month they work. They can then use the sick leave time any time throughout the year. Any unused time goes into a sick bank account that they or other employees can use in the case of emergencies. The human resources department has determined that the amount of unused sick time for individual employees is uniformly distributed between 0 and 480 minutes. The company has decided to give a cash payment to any employee that returns over a specified amount of sick leave minutes. Assuming that the company wishes no more than 5 percent of all employees to get a cash payment, what should the required number of minutes be?

An electronics repair shop has determined that the time between failures for a particular electronic component part is exponentially distributed with a mean time between failures of 200 hours. Based on this information, the probability that a part will fail in the first 20 hours is approximately 0.095.

Watersports Rental at Flathead Lake rents jet skis and power boats for day use. Each piece of equipment has a clock that records the time that it was actually in use while rented. The company has observed over time that the distribution of time used is normally distributed with a mean of 3.6 hours and a standard deviation equal to 1.2 hours. Watersports management has decided to give a rebate to customers who use the equipment for only a short amount of time. They wish to grant a rebate to no more than 10 percent of all customers. Based on the information provided, the amount of time that should be set as the cut-off between getting the rebate and not getting the rebate is approximately 2.06 hours.

A manufacturer advertised that the time it takes a person to assemble a bookcase has been shown to be normally distributed with a mean equal to 125 minutes with a standard deviation equal to 20 minutes. Given this information, the probability that it will take a randomly selected person more than 105 minutes is about 0.1587.

When graphed, the probability distribution for a discrete random variable looks like a histogram.

A random variable is normally distributed with a mean of -50 and a standard deviation of 10. If an observation is randomly selected from the distribution, what value will be exceeded 85% of the time?

One example of a difference between discrete random variables and continuous random variables is that in a discrete distribution P(x > 2) = P(x ≥ 3) while in a continuous distribution P(x > 2) is treated the same as P(x ≥ 2).

A store sells 6 different models of cell phones and have found that they sell an equal number of each model. The probability distribution that would describe this random variable is called:

Which of the following is not a characteristic of the normal distribution?

Employees at a large computer company earn sick leave in one-minute increments depending on how many hours per month they work. They can then use the sick leave time any time throughout the year. Any unused time goes into a sick bank account that they or other employees can use in the case of emergencies. The human resources department has determined that the amount of unused sick time for individual employees is uniformly distributed between 0 and 480 minutes. Based on this information, what is the probability that an employee will have less than 20 minutes of unused sick time?

One of the basic differences between a uniform probability distribution and a normal probability distribution is that the uniform is symmetrical but the normal is skewed depending on the value of the standard deviation.

The parameters of a normal distribution are the mean and the standard deviation.

A professor noted that the grades of his students were normally distributed with a mean of 75.07 and a standard deviation of 11.65. If only 10 percent of the students received grades of A, what is the minimum score needed to receive an A?

At the West-Side Drive-Inn, customers arrive at the rate of 10 every 30 minutes. The time between arrivals is exponentially distributed. Given this, what is the mean time between arrivals?

The transportation manager for the State of New Jersey has determined that the time between arrivals at a toll booth on the state's turnpike is exponentially distributed with λ = 4 cars per minute. Based on this information, what is the probability that the time between any two cars arriving will exceed 11 seconds?

A study of cars arriving at a parking structure at the local airport shows that the time between arrivals is 1.2 minutes and is exponentially distributed. Based on this information, the mean number of cars arriving per minute is about 0.83.

For a standardized normal distribution, determine a value, say z0, so that P(0 < z < z0) = 0.4772.

In comparing a uniform distribution with a normal distribution where both distributions have the same mean and the same range, explain which distribution will have the larger standard deviation.