Exam 8: Further Topics in Probability and Data Description

If the probability of success on each trial of an experiment is 0.8, what is the probability of 6 successes in 10 independent trials? Round your answer to four decimal places. ​

Determine c, if possible, so that the formula describes a discrete probability distribution. ​

If a die is rolled 113 times, what is the probability that a 1 will occur 30 times? Round your answer to four decimal places. ​​

Find the mode of the set of scores. ​ 6, 11, 12, 6, 7, 5, 6, 5 ​

If the probability that a newborn child is a male is , what is the expected number of male children in a family having 2 children? Round your answer to two decimal places. ​

The following bar graph shows the size of the average farm (in acres) for selected years from 1940 to 2000. Which table shows the data displayed in the graph? ​ ​

A baseball player has a lifetime batting average of 0.3. If he comes to bat 7 times in a given game, what is the probability that he will get more than 3 hits? Round your answer to six decimal places. ​

In a certain school district, 23% of the faculty use none of their sick days in a school year. Find the probability that 4 faculty members selected at random used no sick days in a given year. Round your answer to eight decimal places. ​

Suppose the Circuitown buys plasma televisions in sets of 1500. If a television is defective with probability 0.01, what is the probability that at least 24 televisions will be defective in a set? Round your answer to four decimal places. ​

Suppose it has been determined empirically that a certain cell will survive for a given period of time is 0.2. What is the probability that at most 280 of 1500 of these cells will survive for this period of time? Round your answer to four decimal places. ​

Suppose a population of scores x is normally distributed with and . Use the standard normal distribution to find . Round your answer to four decimal places. ​

In a certain community, 45% of the population is Jewish. A study shows that of 12 social service agencies, 4 have board presidents who are Jewish. Find the probability that this could happen by chance. Round your answer to six decimal places. ​

A young man plans to sell umbrellas at the city's Easter Parade. He knows that he can sell 152 umbrellas at $14 each if it rains hard, he can sell 108 if it rains lightly, and he can sell 41 if it doesn't rain at all. Past records show it rains hard 28% of the time on Easter, rains lightly 69% of the time, and does not rain at all 3% of the time. If he can buy 0, 100, or 200 umbrellas at $5 each and return the unsold ones for $3 each, how many should he buy? ​

A candidate must decide whether he should spend his time and money on TV commercials or making personal appearances. His staff determines that by using TV he can reach 110,000 people with probability 0.06, 55,000 people with probability 0.39, and 30,000 people with probability 0.55; by making personal appearances he can reach 80,000 people with probability 0.04, 60,000 people with probability 0.36, and 25,000 people with probability 0.6. In the following table, x represents the number of people reached by each choice. In each case, find the expected value of x to decide which method, if either, will reach more people. ​ ​

Which frequency histogram best describes the data given in the frequency table? ​ ​

Suppose a population of scores x is normally distributed with and . Use the standard normal distribution to find . Round your answer to four decimal places. ​

Suppose a television show rating of 6.4 means that 6.4% of the 110 million TV households watched the show. If a sample of 123 local TV households were queried, what is the probability that more than 9 would have watched the show? Round your answer to four decimal places. ​

A car owner must decide whether she should take out a $100-deductible collision policy in addition to her liability insurance policy. Records show that each year, in her area, 17% of the drivers have an accident that is their fault or for which no fault is assigned, and that the average cost of repairs for these types of accidents is $1200. If the $100-deductible collision policy costs $100 per year, would she save money in the long run by buying the insurance or "taking the chance"? (Hint: Find the expected values if she has the policy and if she doesn't have the policy and compare them.) ​

In a binomial experiment find the probability of fewer than 13 successes in 110 trials if . Round your answer to four decimal places. ​

A bag contains 6 red balls and 6 black balls. We draw 6 balls, with each one replaced before the next is drawn. What is the probability that at least 4 black balls will be drawn? Round your answer to five decimal places. ​