Exam 8: Probability Distributions and Statistics

Steffi feels that the odds in favor of her winning her tennis match tomorrow are 5 to 4. What is the (subjective) probability that she will win her match tomorrow? Give your answer to four decimal places, if necessary. The probability is __________.

Suppose a probability distribution of a random variable X is represented by the accompanying histogram. Shade that part of the histogram whose area gives the probability . ​ ​

A panel of 50 economists was asked to predict the average prime interest rate for the upcoming year. The results of the survey follow. Based on this survey, what does the panel expect the average prime interest rate to be next year? Give your answer to three decimal places, if necessary. E = __________

A panel of 64 economists was asked to predict the average unemployment rate for the upcoming year. The results of the survey follow: On the basis of this survey, what does the panel expect the average unemployment rate to be next year?

If a player placed a $5 bet on red and a $3 bet on black in a single play in American roulette, what would be the expected value of his winnings? Round your answer to the nearest cent. ________ cents

The manager of a certain toy company has decided to accept a shipment of electronic games if there be no more than 3 defective electronic games in a random sample of 20. What is the probability that he will accept the shipment if 5% of the electronic games is defective? ​

Give the range of values that the random variable X may assume and classify the random variable as finite discrete, infinite discrete, or continuous. X = The distance a commuter travels to work

Suppose X is a normal random variable with and Find the value of the following, to four decimal places if necessary. __________ __________ __________

The number of Americans without health insurance, in millions, from 1995 through 2002 is summarized in the following table. What is the standard deviation of Americans without health insurance in the period from 1995 through 2002?

Based on past experience, the manager of the VideoRama Store has compiled the following table, which gives the probabilities that a customer who enters the VideoRama Store will buy 0, 1, 2, 3, or 4 videocassettes. How many videocassettes can a customer entering this store be expected to buy? Give your answer to two decimal places, if necessary. E = __________

Let Z be the standard normal variable. Find the value of z if z satisfies . ​

The mean annual starting salary of a new graduate in a certain profession is $43,000 with a standard deviation of $500. What is the probability that the starting salary of a new graduate in this profession will be between $41,500 and $44,500? Give your answer as a fraction.

The minimum age requirement for a regular driver's license differs from state to state. The frequency distribution for this age requirement in the 50 states is: Compute the mean, variance, and standard deviation of the random variable X.

Use the appropriate normal distribution to approximate the resulting binomial distribution. An experiment was conducted to test the effectiveness of a new drug in treating a certain disease. The drug was administered to 50 mice that had been previously exposed to the disease. It was found that 30 mice subsequently recovered from the disease. It was determined that the natural recovery rate from the disease is 0.5. Determine the probability that 30 or more of the mice not treated with the drug would recover from the disease.

Find the value of the probability of the standard normal variable Z corresponding to this area.

The manager of C & R Clothiers, a major manufacturer of men's shirts, has determined that 3% of C & R's shirts do not meet with company standards and are sold as "seconds" to discount and outlet stores. What is the probability that in a day's production of 200 dozen shirts, less than 12 dozen will be classified as "seconds"? ​ Round your answer to four decimal places, if necessary. ​ __________

According to data released by the Chamber of Commerce of a certain city, the weekly wages (in dollars) of female factory workers are normally distributed with a mean of 575 and a standard deviation of 50. Find the probability that a female factory worker selected at random from the city makes a weekly wage of $550 to $625. ​

The probability distribution of the random variable X is shown in the accompanying table.

Sugar packaged by a certain machine has a mean weight of 3 lb and a standard deviation of 0.02 lb. For what values of c can the manufacturer of the machinery claim that the sugar packaged by this machine has a weight between 3 - c and 3 + c lb with probability at least 96%? __________ lb

Give the range of values that the random variable X may assume and classify the random variable as finite discrete, infinite discrete, or continuous. X = The number of times an accountant takes the CPA examination before passing