Exam 5: Discrete Probability Distributions

Find the indicated probability. Round to three decimal places. -In a study, 38% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people living close to a nuclear power plant. Among 12 adults randomly selected from this area, only 3 reported that their health was excellent. Find the probability that when 12 adults are randomly selected, 3 or fewer are in excellent health.

Find the indicated probability. Round to three decimal places. -A test consists of 10 true/false questions. To pass the test a student must answer at least 9 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. - $\mathrm { n } = 6 , \mathrm { x } = 3 , \mathrm { p } = \frac { 1 } { 6 }$

Find the standard deviation, ?, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $n = 2649 ; p = 0.63$

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 $P ( x ) = p ( 1 - p ) ^ { x - 1 }$ , where p is the probability of success on any one trial.Assume that the probability of choosing a yellow piece of candy in a bag of hard candy is 0.240. Find the probability that the first yellow candy is found in the fourth inspected. Round your answer to the nearest thousandth.

The probability that a person has immunity to a particular disease is 0.3. Find the mean number who have immunity in samples of size 16.

Helene claimed that the expected value when rolling a fair die was 3.5. Steve said that wasn't possible. He said that the expected value was the most likely value in a single roll of the die, and since it wasn't possible for a die to turn up with a value of 3.5, the expected value couldn't possibly be 3.5. Who is right?

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 µ - 2? or greater than µ + 2?. -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 684 consumers who recognize the Dull Computer Company name?

Anna uses the letter X to represent the possible sequences of heads and tails that can be obtained when a coin is flipped three times. The possible sequences together with their probabilities are listed below: Probability of sequence HHH 1/8 HHT 1/8 HTH 1/8 HTT 1/8 THH 1/8 THT 1/8 TTH 1/8 TTT 1/8 Is X a random variable? Why or why not? If it is not, which associated variable is a random variable? Give the probability distribution of the associated random variable.

Previously, you learned to find the three important characteristics of data: the measure of central tendency, the measure of variation, and the nature of the distribution. We can find the same three characteristics for a binomial distribution. Given a binomial distribution with $\mathrm { p } = 0.4 \text { and } \mathrm { n } = 8 \text {, find the three characteristics. }$

Find the mean of the given probability distribution. -The accompanying table shows the probability distribution for $x$ , the number that shows up when a loaded die is rolled. x P(x) 1 0.12 2 0.15 3 0.13 4 0.11 5 0.12 6 0.37

A multiple choice test has 7 questions each of which has 5 possible answers, only one of which is correct. If Judy, who forgot to study for the test, guesses on all questions, what is the probability That she will answer exactly 3 questions correctly?

Find the mean of the given probability distribution. - () 0 0.23 1 0.20 2 0.37 3 0.06 4 0.14

Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5.00 for rolling a 1 or a 2, nothing otherwise. What is your expected value?

Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. - $\mathrm { n } = 32 ; \mathrm { p } = 3 / 5$

The probability of winning a certain lottery is $\frac { 1 } { 64,481 }$ . For people who play 669 times, find the standard deviation for the number of wins.

Identify the given random variable as being discrete or continuous. -The number of phone calls between New York and California on Thanksgiving day

Find the mean of the given probability distribution. -The number of golf balls ordered by customers of a pro shop has the following probability distribution. x P(x) 3 0.14 6 0.22 9 0.36 12 0.18 15 0.10

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places. - $n = 10 , x = 2 , p = \frac { 1 } { 3 }$

In a certain town, 40% of adults have a college degree. The accompanying table describes the probability distribution for the number of adults (among 4 randomly selected adults) who have a college degree. Find the standard deviation for the probability distribution. () 0 0.1296 1 0.3456 2 0.3456 3 0.1536 4 0.0256