Exam 8: Further Topics in Probability and Data Description

A multiple-choice test has 28 questions and 3 choices for each question. If a student is totally unprepared and guesses on each question, what is the probability that she will answer 15 questions correctly? Round your answer to four decimal places. ​

Probabilities from a binomial probability distribution with trials and with the probability of success on each trial equal to can be approximated by using a normal distribution.​ ​

The heights of a certain species of plant are normally distributed, with mean 22 cm and standard deviation 4 cm. What is the probability that a plant chosen at random will be will be between 18 and 26 cm tall? Round your answer to four decimal places. ​

The mean weight of a group of boys is 150 lb, with a standard deviation of 20 lb. If the weights are normally distributed, find the probability that one of the boys picked at random from the group weighs more than 178 lb. Use a table of the standard normal distribution to solve the problem. Round your answer to four decimal places. ​

Use a table of the standard normal distribution to find the probability that a z-score from the standard normal distribution will lie within the interval . Round your answer to four decimal places. ​

Suppose that 8% of the patients who have a certain disease will die from it. If 80 people have the disease, how many would we expect to die from it, and what is the standard deviation of the number of deaths that could occur? Round any estimated quantities to two decimal places. ​

Find the mean of the following data. Round your answer to the nearest integer. ​

It has been determined empirically that the probability that a given cell will survive for a given period of time is 0.65. Find the probability that 3 out of 7 of these cells will survive for this period of time. Round your answer to six decimal places. ​

A family has 5 children. If the probability that each child is a girl is 0.5, what is the probability that 4 of the children are girls? Round your answer to six decimal places. ​

If the ratio of boys born to girls born is 75 to 60, and if 17 children are born in a certain hospital in a day, what is the probability that 6 of them are boys? Round your answer to six decimal places. ​

The birth weights (in kilograms) of a sample of 160 children are given in the following table. What is the mean of the weights? Round your answer to two decimal places. ​

Find the mode of the following data. Round your answer to the nearest integer. ​ Interval Frequency 5 9 4 2 3

Estimate the variance for the following probability distribution to two decimal places. ​

If a die is rolled 39 times, what is the probability that a 6 will occur at least 12 times? Round your answer to four decimal places. ​

Suppose the Rent-to-Own Company estimates that 30% of its rentals result in a sale of the product. If the company rents 13,000 of its product in a year, what is the probability that it will sell at most 4,000 of its products? Round your answer to four decimal places. ​

If a fair die is rolled 7 times, what is the probability that an odd number will result 4 times? ​

Suppose that a student is offered a chance to draw a card from an ordinary deck of 52 playing cards and win $18 for an ace, $8 for a king, and $1 for a queen. If $5 must be paid to play the game, what is the expected loss every time the game is played by the student? ​

Determine y, if possible, so that the table describes a discrete probability distribution. ​ X P(x) 1 2 3 4 Y ​

Suppose that AudioMart has a secret sale released only on the Internet because management thought that word-of-mouth publicity about the sale would result in 5% of U.S. households recognizing the company name. If this is true, what is the probability that at least 100 of 2000 people surveyed recognize the company name? Round your answer to four decimal places. ​

Reaction time for a group of people is normally distributed, with a mean of 0.6 seconds and a standard deviation of 0.2 seconds. Find the probability that an individual selected at random has a reaction time less than 0.9 seconds. Round your answer to four decimal places. ​