Exam 12: Binomial Distributions

If X has a binomial distribution with 20 trials and a mean of 6, then the success probability p is:

A local politician claims that one in five automobile accidents involve a teenage driver. He is advocating increasing the age at which teenagers can drive alone. Over a two-month period there are 67 accidents in your city, and only nine of them involve a teenage driver. If the politician is correct, what is the chance that you would observe nine or fewer accidents involving a teenage driver?

Zener cards are often used to test the psychic ability of individuals. In the Zener deck, there are five different patterns displayed and each has a 1/5 probability of being drawn from a well-shuffled deck. The five patterns are: circle, plus sign, wavy lines, empty box, and star. One hundred trials were conducted, and your very impressive friend guessed right on 41 of those trials. What proportion of the cards would I expect my friend to guess correctly?

Twenty percent of American households own three or more cars. A random sample of 144 American households is selected. Let X be the number of households selected that own three or more cars. Using the Normal approximation, the probability that at least 34 of the households selected own at least three or more cars is:

An experiment consisted of 10 draws with replacement from an urn containing four red marbles and six green marbles. The probability that there are at least three and at most six red marbles is:

Two students taking a multiple choice exam with 20 questions and four choices for each question have the same incorrect answer on eight of the problems. The probability that student B guesses the same incorrect answer as student A on a particular question is 1/4. If the student is guessing, it is reasonable to assume guesses for different problems are independent. The instructor for the class suspects the students exchanged answers. The teacher decides to present a statistical argument to substantiate the accusation. A possible model for the number of incorrect questions that agree is:

A local veterinary clinic typically sees 15% of its horses presenting with West Nile virus. If 10 horses are admitted during July, what is the probability at least one of the 10 horses has been infected with West Nile virus?

Zener cards are often used to test the psychic ability of individuals. In the Zener deck, there are five different patterns displayed and each has a 1/5 probability of being drawn from a well-shuffled deck. The five patterns are: circle, plus sign, wavy lines, empty box, and star. One hundred trials were conducted, and your very impressive friend guessed right on 41 of those trials. Given this sample, can we use the Normal approximation to the binomial?

A small class has 10 students. Seven of the students are male and three are female. You write the name of each student on a small card. The cards are shuffled thoroughly, and you choose one at random, observe the name of the student, and replace it in the set. The cards are thoroughly reshuffled, and you again choose a card at random, observe the name, and replace it in the set. This is done a total of five times. Let X be the number of cards observed in these five trials with a name corresponding to a male student. The random variable X has which of the following probability distributions?

A very large gardening business grows rose bushes for sale to garden stores around the world. The most popular colors are red, pink, and white. The business decides on 50% red roses, 30% pink, and 20% white. A gardener orders 10 rose bushes selected randomly from a huge field. Her primary interest is in pink roses. Assuming rose bushes are selected independently, the number of pink rose bushes can be modeled by a binomial distribution. The probability of getting 1 pink rose bush is:

Suppose we select an SRS of size n = 100 from a large population having proportion p of successes. Let X be the number of successes in the sample. For which value of p would it be safe to assume the sampling distribution of X is approximately Normal?

Which of the following statements is not true about the binomial distribution?

A local veterinary clinic typically sees 15% of its horses presenting with West Nile virus. If 10 horses are admitted during July, what is the probability that 2 or fewer horses among the 10 horses admitted have been infected with West Nile virus?

Suppose X is a random variable with the binomial distribution with n = 4 and p = 1/4. The probability that X is greater than or equal to 1 is:

A very large gardening business grows rose bushes for sale to garden stores around the world. The most popular colors are red, pink, and white. The business decides on 50% red roses, 30% pink, and 20% white. A gardener orders 10 rose bushes selected randomly from a huge field. Her primary interest is in pink roses. A good model for the number of bushes with pink roses is:

An article in Parenting magazine reported that 60% of Americans needed a vacation after visiting their families for the holidays. Suppose this is the true proportion of Americans who feel this way. A random sample of 100 Americans is taken. Using the Normal approximation, what is the probability that less than 50% of the people in the sample feel that they need a vacation after visiting their families for the holidays?

Which of the following statements is true about a binomial experiment?

For which of the following counts would a binomial probability model be reasonable?

A very large gardening business grows rose bushes for sale to garden stores around the world. The most popular colors are red, pink, and white. The business decides on 50% red roses, 30% pink, and 20% white. A gardener orders 10 rose bushes selected randomly from a huge field. Her primary interest is in pink roses. Assuming rose bushes are selected independently, we can use the binomial distribution for calculations. The probability of getting at least 3 pink rose bushes is: