Exam 6: Introduction to Continuous Probability Distributions

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 manager at a local movie theater has collected data for a long period of time and has concluded that the revenue from concession sales during the first show each evening is normally distributed with a mean equal to $336.25 and a standard deviation equal to $80.Based on this information,what are the chances that the revenue on the first show will be between $300 and $500?

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?

If 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 the time it takes for a randomly selected customer to be served will be less than 5 minutes is 0.40.

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?

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 not fail in the first 200 hours is 0.50.

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:

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.Based on this information we can conclude that 90 percent of the fillets weight more than 1.0 pound.

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.If 2 trees are randomly chosen,the probability that both trees will have grown more than 20 inches during the year is approximately .037.

A class takes an exam where the average time to complete the exam is normally distributed with a time of 40 minutes and standard deviation of 9 minutes.If the class lasts 1 hour,what percent of the students will have turned in the exam after 60 minutes?

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.

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

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:

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?

In a standard normal distribution,the probability that Z is greater than 0.5 is

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.

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?

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?

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.

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.