Exam 5: Discrete Probability Distributions

In a game, you have a 1/20 probability of winning $76 and a 19/20 probability of losing $9. What is your expected value?

Focus groups of 11 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 5.7, and The standard deviation is 0.50. Would it be unusual to randomly select 11 people and find that Greater than 9 recognize the Famous brand name?

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. -If a person is randomly selected from a certain town, the probability distribution for the number, x, of siblings is as described in the accompanying table. () 0 0.27 1 0.28 2 0.23 3 0.10 4 0.06 5 0.02

Find the indicated probability. Round to three decimal places. -Find the probability of at least 2 girls in 8 births. Assume that male and female births are equally likely and that the births are independent events.

A company manufactures batteries in batches of 22 and there is a 3% rate of defects. Find the variance for the number of defects per batch.

Use the given values of n and p to find the minimum usual value $\mu - 2 \sigma \text { and the maximum usual value } \mu + 2 \sigma$ . Round your answer to the nearest hundredth unless otherwise noted. - $n = 659 , p = \frac { 4 } { 5 }$

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 exactly 4 girls.

Find the mean of the given probability distribution. -A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.45, 0.37, 0.17, and 0.01, respectively.

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 $\mu - 2 \sigma \text { or greater than } \mu + 2 \sigma$ -The Acme Candy Company claims that 8% of the jawbreakers it produces actually result in a broken jaw. Suppose 9571 persons are selected at random from those who have eaten a jawbreaker produced at Acme Candy Company. Would it be unusual for this sample of 9571 to contain 806 persons with broken jaws?

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - $\mathrm { n } = 625 ; \mathrm { p } = 0.7$

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. - () 0 0.246 1 0.148 2 0.213 3 0.167 4 0.247 5 0.142

Use the given values of n and p to find the minimum usual value $\mu - 2 \sigma$ and the maximum usual value $\mu + 2 \sigma$ . Round your answer to the nearest hundredth unless otherwise noted. - $n = 460 , p = \frac { 2 } { 7 }$

Sampling without replacement involves dependent events, so this would not be considered a binomial experiment. Explain the circumstances under which sampling without replacement could be considered independent and, thus, binomial.

Assume that a probability distribution is described by the discrete random variable x that can assume the values 1, 2, . . . , n; and those values are equally likely. This probability has mean and standard deviation described as follows: $\mu = \frac { n + 1 } { 2 } \text { and } \sigma = \sqrt { \frac { n ^ { 2 } - 1 } { 12 } }$ $\text { Show that the formulas hold for the case of }n=7$

Find the indicated probability. -Suppose that 10% of people are left handed. If 6 people are selected at random, what is the probability that exactly 2 of them are left handed?