Exam 5: Probability Distributions

Focus groups of 10 people are randomly selected to discuss products of the Famous Company. It is determined that the mean number (per group)who recognize the Famous brand name is 4.8, and the standard deviation is 0.73. Would it be unusual to randomly select 10 people and find that greater than 8 recognize the Famous brand name?

Assume that there is a 0.15 probability that a basketball playoff series will last four games, a 0.30 probability that it will last five games, a 0.25 probability that it will last six games, and a 0.30 probability that it will last seven games. Is it unusual for a team to win a series in 5 games?

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth - $n = 2466 ; p = .63$

If the random variable x has a Poisson Distribution with mean µ = 2, find the probability that x = 1.

Solve the problem. -The random variable x is the number of houses sold by a realtor in a single month at the Sendsom's Real Estate Office. Its probability distribution is as follows. Find the standard deviation for the probability distribution. Houses Sold () Probability P(x) 0 0.24 1 0.01 2 0.12 3 0.16 4 0.01 5 0.14 6 0.11 7 0.21

Let the random variable x represent the number of boys in a family of three children. Construct a table describing the probability distribution, then find the mean and standard deviation.

Assume that a researcher randomly selects 14 newborn babies and counts the number of girls selected, x. The probabilities corresponding to the 14 possible values of x are summarized in the given table. Answer the question using the table. Probabilities of Girls x( girls ) P(x) x( girls) P(x) x( girls) P(x) 0 0.000 5 0.122 10 0.061 1 0.001 6 0.183 11 0.022 2 0.006 7 0.209 12 0.006 3 0.022 8 0.183 13 0.001 4 0.061 9 0.122 14 0.000 -Find the probability of selecting 2 or more girls.

Solve the problem. -Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5.00 for rolling a 3 or a 6, nothing otherwise. What is your expected value?

Find the standard deviation, ?, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. -n = 36; p = .2

Solve the problem. -On a multiple choice test with 24 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the variance for the number of correct answers.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -n = 5, x = 2, p = 0.70

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. - () 1 0.037 2 0.200 3 0.444 4 0.296

If a procedure meets all the conditions of a binomial distribution except that the number of trials is not fixed, then the geometric distribution can be used. The probability of getting the first success on the xth trial is given by Pchoosing a yellow piece of cand x = p 1 - px - 1 , where p is ty in a bag of hard candhe probability of succey is ss on any on0.204. Find the e trial. probAssuame that thbility that e probathe first yellow bility of candy is found in the fourth inspected.

Use the given values of n and p to find the minimum usual value µ - 2? and the maximum usual value µ + 2? -n = 252, p = 0.261

Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than $\mu - 2 \sigma$ or greater than $\mu + 2 \sigma$ . -A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual to get 687 consumers who recognize the Dull Computer Company name?

Provide an appropriate response. -List the four requirements of a Poisson distribution.

Identify the given random variable -The pH level in a shampoo

Use the given values of n and p to find the minimum usual value µ - 2? and the maximum usual value µ + 2? -n = 48; p = .4

A computer salesman averages 1.9 sales per week. Use the Poisson distribution to find the probability that in a randomly selected week the number of computers sold is 3.

Solve the problem. -In a game, you have a 1/42 probability of winning $67 and a 41/42 probability of losing $7. What is your expected value?