Exam 6: Introduction to Continuous Probability Distributions

Typically,a continuous random variable is one whose value is determined by measurement instead of counting.

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,the average time between arrivals is:

It is assumed that the time failures for an electronic component are exponentially distributed with a mean of 50 hours between consecutive failures.If one extra component is installed as a backup,what is the probability of at least one of the two components working for at least 60 hours?

The makers of Sweet-Things candy sell their candy by the box.Based on company policy,the mean target weight of all boxes is 2.0 pounds.To make sure that they are not putting too much in the boxes,the manager wants no more than 3 percent of all boxes to contain more than 2.10 pounds of candy.In order to do this,what should the mean fill weight be set to if the fill standard deviation is 0.13 pounds? Assume that the box weights are normally distributed.

Suppose the time it takes for a customer to be served at a fast-food chain business is thought to be uniformly distributed between 3 and 8 minutes,then the probability that it will take exactly 5 minutes is 0.20.

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?

Suppose the time it takes for a customer to be served at a fast-food chain business is thought to be uniformly distributed between 3 and 8 minutes,then the probability that a customer is served in less than 3 minutes is 0.

Any normal distribution can be converted to a standard normal distribution.

The manager of a computer help desk operation has collected enough data to conclude that the distribution of time per call is normally distributed with a mean equal to 8.21 minutes and a standard deviation of 2.14 minutes.The manager has decided to have a signal system attached to the phone so that after a certain period of time,a sound will occur on her employees' phone if she exceeds the time limit.The manager wants to set the time limit at a level such that it will sound on only 8 percent of all calls.The time limit should be:

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

Suppose that it is believed that investor returns on equity investments at a particular brokerage house are normally distributed with a mean of 9 percent and a standard deviation equal to 3.2 percent.What percent of investors at this brokerage house earned at least 5 percent?

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 between 20 and 100 hours is approximately 0.30.

A randomly selected value from a normal distribution is found to be 2.1 standard deviations above its mean.What is the probability that a randomly selected value from the distribution will be greater than 2.1 standard deviations above the mean?

A random variable is normally distributed with a mean of 25 and a standard deviation of 5.If an observation is randomly selected from the distribution,what value will be exceeded 10% of the time?

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

It is assumed that the time failures for an electronic component are exponentially distributed with a mean of 50 hours between consecutive failures.Based on this information,what is the probability that a randomly selected part will fail in less than 10 hours?

Students who have completed a speed reading course have reading speeds that are normally distributed with a mean of 950 words per minute and a standard deviation equal to 220 words per minute.Based on this information,what is the probability of a student reading at more than 1400 words per minute after finishing the course?

A recent study showed that the length of time that juries deliberate on a verdict for civil trials is normally distributed with a mean equal to 12.56 hours with a standard deviation of 6.7 hours.Given this information,what is the probability that a deliberation will last between 10 and 15 hours?

The time between calls to an emergency 911-call center is exponentially distributed with a mean time between calls of 645 seconds.Based on this information,what is the probability that the time between the next two calls is between 200 and 400 seconds?

For a continuous distribution the total area under the curve is equal to 100.