Exam 6: Introduction to Continuous Probability Distributions

Service time for customers at a drive-through coffee shop has been shown to be uniformly distributed between 2 and 10 minutes.Customers will complain when service time exceeds 7.5 minutes.Based on this information,the probability of getting a complaint based on service time is 0.3125.

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 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 vehicle speeds on a city street have been determined to be normally distributed with a mean of 33.2 mph and a variance of 16.Based on this information,the probability that if three randomly selected vehicles are monitored and that two of the three will exceed the 35 mph speed limit is slightly greater than 0.18.

The normal distribution is one of the most frequently used discrete probability distributions.

What is the difference between a normal distribution and the standard normal distribution?

If a continuous random variable is said to be exponentially distributed,what would be the easiest way to reduce the standard deviation?

All symmetric distributions can be assumed normally distributed.

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 400 minutes of sick leave at the end of the year.What percentage of employees could expect a cash payment?

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

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

The time it takes a parent to assemble a children's bicycle has been shown to be normally distributed with a mean equal to 295 minutes with a standard deviation equal to 45 minutes.Given this information,the probability that it will take a randomly selected parent more than 220 minutes is about 0.0475.

The fares received by taxi drivers working for the City Taxi line are normally distributed with a mean of $12.50 and a standard deviation of $3.25.Suppose a driver has four consecutive fares that are less than $6.00.What is the probability of this happening?

A major cell phone service provider has determined that the number of minutes that its customers use their phone per month is normally distributed with a mean equal to 445.5 minutes with a standard deviation equal to 177.8 minutes.The company is thinking of changing its fee structure so that anyone who uses the phone less than 250 minutes during a given month will pay a reduced monthly fee.Based on the available information,what percentage of current customers would be eligible for the reduced fee?

If a uniform distribution and normal distribution both have the same mean and the same range,the normal distribution will have a larger standard deviation than the uniform distribution

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.

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 spend more than 9 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.Based on this information,what is the probability that three randomly chosen employees have over 400 unused sick minutes at the end of the year?

It is assumed that the time failures for an electronic component are exponentially distributed with a mean of 50 hours between consecutive failures.What is the probability that a component will be functioning after 60 hours?

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