Exam 6: Introduction to Continuous Probability Distributions

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.If two students were selected at random,what is the probability that they would both read at less than 400 words per minute?

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.

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?

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

For a standardized normal distribution,determine a value,say z₀,so that P(z > z₀)= 0.025.

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,the standard deviation for the time between arrivals is:

The actual weight of 2-pound sacks of salted peanuts is found to be normally distributed with a mean equal to 2.04 pounds and a standard deviation of 0.25 pounds.Given this information,the probability of a sack weighing more than 2.40 pounds is 0.4251.

A random variable,x,has a normal distribution with μ = 13.6 and σ = 2.90.Determine a value,x₀,so that P(x > x₀)= 0.05.

The standard normal distribution table provides probabilities for the area between the z-value and the population mean.

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?

Assuming that the change in daily closing prices for stocks on the New York Stock Exchange is a random variable that is normally distributed with a mean of $.35 and a standard deviation of $.33.Based on this information,what is the probability that a randomly selected stock will close up $.75 or more?

For the normal distribution with parameters μ = 5,σ = 4;calculate P(0 < x < 8).

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.

The State Department of Forests has determined that annual tree growth in a particular forest area is normally distributed with a mean equal to 17 inches and a standard deviation equal to 6 inches.Based on this information,it is possible for a randomly selected tree not to have grown any during a year.

In a standard normal distribution,the probability P(-1.00< z < 1.20)is the same as:

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.

It is thought that the time between customer arrivals at a fast food business is exponentially distributed with λ equal to 5 customers per hour.Given this information,what is the mean time between arrivals?

The Varden Packaging Company has a contract to fill 50-gallon barrels with gasoline for use by the U.S.Army.The machine that Varden uses has an adjustable device that allows the average fill per barrel to be adjusted as desired.However,the actual distribution of fill volume from the machine is known to be normally distributed with a standard deviation equal to 0.5 gallons.The contract that Varden has with the military calls for no more than 2 percent of all barrels to contain less than 49.2 gallons of gasoline.In order to meet this requirement,Varden should set the mean fill to approximately 50.225 gallons.

A seafood shop sells salmon fillets where the weight of each fillet is normally distributed with a mean of 1.6 pounds and a standard deviation of 0.3 pounds.They want to classify the largest fillets as extra large and charge a higher price for them.If they want the largest 15 percent of the fillets to be classified as extra large,the minimum weight for an extra large fillet should be 1.91 pounds.

For a standardized normal distribution,calculate P(0.00 < z < 2.33).