Exam 5: Continuous Random Variables and Probability Distributions

You are the Webmaster for your firm's Website.From your records,you know that the probability that a visitor will buy something from your firm is 0.23.If the number of visitors in one day is 952,what is the probability that less than 200 of them will buy something from your firm? Use the normal approximation for the binomial.

For a normal distribution,practically all the area under the normal curve is within plus or minus three standard deviations from the mean.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let the random variable X follow a normal distribution with a mean of 61.7 and a standard deviation of 5.2. -What is the value of k such that P(X > k)= 0.63?

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. -With probability 0.09 the number of successes is less than how many?

If the random variable Z follows a standard normal distribution,then = 1.

If Z is a standard normal random variable,the area between Z = 0.0 and Z =1.20 is 0.3849,while the area between Z = 0.0 and Z = 1.40 is 0.4192.What is the area between Z = -1.20 and Z = 1.40?

Let the random variable Z follow a standard normal distribution.Find the value k,such that P(Z > k)= 0.73.

Suppose X is a normal random variable with mean of 70 and standard deviation of 4.The Z-score was calculated for a number,and it was 2.85.What is X?

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. -With probability 0.20,the number of successes is greater than how many?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Sales at a local wholesaler consist of both retail as well as online sales.During the course of a month,retail sales have a mean of $96,780 with a standard deviation of $12,520.Over the same time period,online sales average $229,620 with a standard deviation of $23,100.Assume that the retail sales are independent of online sales. -What is the standard deviation of the wholesaler monthly sales?

The probability that a random variable lies between a pair of values is the area under the probability density function to the left of the two values.

Investment A has an expected return of 10% with a standard deviation of 3.5%.Investment B has an expected return of 6% with a standard deviation of 1.2%.If you invest equally in both investments,what is the expected return and standard deviation of your portfolio? What assumptions have you made?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let the random variable Z follow a standard normal distribution. -What is P(Z > 0.29)?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: You have recently joined a country club.The number of times you expect to play golf in a month is represented by a random variable with a mean of 10 and a standard deviation of 2.2.Assume you pay monthly membership fees of $500 per month and pay an additional $50 per round of golf. -What is the standard deviation for your average monthly bill from the country club?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The life of a new type of light bulb is uniformly distributed between 1,200 and 1,600 hours. -The probability is 70% that a randomly-selected light bulb will last at least how long.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The time it takes to assemble an electronic component is normally distributed with a mean of 17.2 minutes and a standard deviation of 3.1 minutes. -The probability is 95% that it will take at least how long to assemble a component?

Let the random variable Z follow a standard normal distribution.Find P(-1.33 < Z < 0.78).

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let the random variable X follow a normal distribution with a mean of 61.7 and a standard deviation of 5.2. -What is the value of k such that P(59 < X < k)= 0.54?

The probability density function for the exponential distribution is bell-shaped and symmetrical around the mean λ.

When we convert normal distributions to the standard normal distribution,we are essentially making them all alike.How is this possible and what are the implications?