Exam 5: Continuous Random Variables and Probability Distributions

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose that the time between successive occurrences of an event follows an exponential distribution with mean 1/λ minutes.Assume that an event occurs. -Show that,if 4 minutes have already elapsed,the probability that a further 4 minutes will elapse before the next occurrence is e^-8λ.Explain your answer in words.

If Z is a standard normal random variable,the area between Z = 0.0 and Z = 1.25 compared to the area between Z = 1.25 and Z = 2.5 will be:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Consider a random sample of size n =1800 from a binomial probability distribution with P = 0.40,and X = number of successes. -Find the probability that the number of successes is between 680 and 750.

We can convert any normal distribution to a distribution with a mean 0 and a variance 1.What is the distribution called?

The binomial distribution and the normal distribution are similar in a number of ways,although they are different distributions.What are the basic differences between the two distributions?

During normal business hours at a gas station,customers arrive,on average,every ten minutes.Assume that the distribution of the time between arrivals follows an exponential distribution.Suppose that a customer has just left the gas station.What is the probability that the cashier at the gas station has more than 15 minutes before the next customer arrive?

If the random variable X follows a binomial distribution with parameters n and P,then when using the normal distribution to approximate the distribution of X,we should use nP for the mean and nP(1-P)for the standard deviation.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The continuous random variable X is uniformly distributed over the interval 4 to 10. -What is the mean of this distribution?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The number of nails in a five-pound box of nails is normally distributed with a mean of 563.3 and a standard deviation of 33.2. -What is the probability that there are between 525 and 575 nails in a randomly-selected five-pound box of nails?

In computing probabilities for proportion or percentage intervals,we use a direct extension of the normal distribution approximation for the:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The continuous random variable X is uniformly distributed over the interval 4 to 10. -What is P(6 ≤ X ≤ 8)?

Suppose that 24% of all sales in a grocery store are for amounts greater than $100.In a random sample of 50 invoices,what is the probability that more than ten of the invoices are for over $100? Use the normal approximation for the binomial distribution.

The length of time it takes to fill an order at a local sandwich shop is normally distributed with a mean of 4.1 minutes and a standard deviation of 1.3 minutes.If the sandwich shop employees make $6.00 an hour,what is the mean and standard deviation for the labor costs per sandwich?

A continuous uniform random variable has a constant probability density function everywhere within the range of values the random variable can take.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose x is normally distributed with a mean of 75 and a standard deviation of 4. -Find the 90^th percentile.

To obtain the probability that a continuous random variable falls in a specified range,we find the difference between the cumulative probabilities at the lower and upper end of the:

In any normal distribution,the mean,median,mode,and standard deviation are all at the same position on the horizontal axis.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A professor sees students during regular office hours.Times spent with students follow an exponential distribution with mean of 12 minutes. -Find the probability that a given student spends between 12 and 15 minutes with the professor.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Consider a random sample of size n =1800 from a binomial probability distribution with P = 0.40,and X = number of successes. -Find the probability that the number of successes is greater than 775.

Which of the following is false regarding the normal distribution?