Exam 8: Probability Distributions and Statistics

One of the key determinants of economic growth is access to capital. Using 54 variables to create an index of 1-7, with 7 been best possible access to capital, Milken Institue ranked the following as the top ten nations (although technically Hong Kong is not a nation) by the ability of their entrepreneurs to gain access to capital: Find the mean of the indices of the top ten nations. What is the standard deviation of these data?

In American roulette a player may bet on a split (two adjacent numbers). In this case, if the player bets $1 and either number comes up, the player wins $17 and gets his $1 back. If neither comes up, he loses his $1 bet. Find the expected value of the winnings on a $1 bet placed on a split. Round your answer to the nearest cent. $ __________

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 35 mice subsequently recovered from the disease. It was determined that the natural recovery rate from the disease is 0.5. Determine the probability that 35 or more of the mice not treated with the drug would recover from the disease. ​ Round your answer to four decimal places, if necessary. ​ The probability is __________.

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 25. What is the probability that he will accept the shipment if 20% of the electronic games is defective? Round the answer to three decimal places, if necessary. The probability is __________.

Find the value of the probability of the standard normal variable Z corresponding to this area. P(- 1.47 < Z < - 0.25)

Use the appropriate normal distribution to approximate the resulting binomial distribution. A coin weighted so that the probability of obtaining a head in a single toss is 0.2 .If the coin is tossed 20 times, what is the probability of obtaining more than 10 heads? (Round your intermediate calculations to 2 decimal places.)

Find the value of the probability of the standard normal variable Z corresponding to this area. P ( Z > 2.31 )

Make a sketch of the area under the standard normal curve corresponding to the given probability. P ( Z > - 1.36 )

Suppose X is a normal random variable with and . Find the value of .

Find the value of the probability of the standard normal variable Z corresponding to the shaded area under the standard normal curve. P ( Z < - 1.76 )

On the average, a student takes 100 words/minute midway through an advanced court reporting course at the American Institute of Court Reporting. Assuming that the dictation speeds of the students are normally distributed and that the standard deviation is 20 words/minute, what is the probability that a student randomly selected from the course can take dictation at a speed between 90 and 120 words/minute?

A buyer for Discount Fashions, an outlet for women's apparel, is considering buying a batch of clothing for $61,000. She estimates that the company will be able to sell it for $80,000, $75,000, or $70,000 with probabilities of 0.30, 0.20, and 0.50, respectively. Based on these estimates, what will be the company's expected gross profit? $ __________

Let Z be the standard normal variable. Find the values of z if z satisfies P (-z < Z < z) = 0.8354

TKK Products manufactures electric light bulbs in the 50-, 60-, 75-, and 100-watt range. Laboratory tests show that the lives of these light bulbs are normally distributed with a mean of 760 hr and a standard deviation of 60 hr. ​ Round your answers to four decimal places, if necessary. ​ What is the probability that a TKK light bulb selected at random will burn for more than 820 hr? ​ __________ ​ What is the probability that a TKK light bulb selected at random will burn for less than 640 hr? ​ __________ ​ What is the probability that a TKK light bulb selected at random will burn between 760 and 820 hr? ​ __________ ​ What is the probability that a TKK light bulb selected at random will burn between 640 and 800 hr? ​ __________

A biology quiz consists of 10 multiple-choice questions. 5 must be answered correctly to receive a passing grade. If each question has 4 possible answers, of which only one is correct, what is the probability that a student who guesses at random on each question will pass the examination? ​

Find the condition on the numbers a and b such that the table below gives the probability distribution of the random variable X. ​

Four cards are drawn from a well-shuffled deck of 52 playing cards. Let X denote the number of aces drawn. Find .

Use the appropriate normal distribution to approximate the resulting binomial distribution. ​ Jorge sells magazine subscriptions over the phone. He estimates that the probability of his making a sale with each attempt is .11. What is the probability of Jorge making more than 10 sales if he makes 80 calls? ​ Round your answer to four decimal places, if necessary. ​ The probability is __________.

The management of MultiVision, a cable TV company, intends to submit a bid for the cable television rights in one of two cities, A or B. If the company obtains the rights to city A, the probability of which is 0.3, the estimated profit over the next 10 yr is $10 million; if the company obtains the rights to city B, the probability of which is 0.4, the estimated profit over the next 10 yr is $7 million. The cost of submitting a bid for rights in city A is $300,000 and that of city B is $300,000. ​ By comparing the expected profits for each venture, determine whether the company should bid for the rights in city A or city B.

If the probability that a certain tennis player will serve an ace is 0.15, what is the probability that he will serve at least three aces out of five serves? Round the answer to three decimal places, if necessary. ​ The probability is __________.