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Exam 5: Discrete Probability Distributions

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Question 31

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Find the indicated probability. Round to three decimal places. -In a study, 44% 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 14 adults randomly selected from this area, only 3 Reported that their health was excellent. Find the probability that when 14 adults are randomly selected, 3 or Fewer are in excellent health.

A) 0.053
B) 0.073
C) 0.020
D) 0.046

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Question 32

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In a survey sponsored by Coca-Cola, subjects aged 15-65 were asked what contributes most to their happiness. The table is based on their responses. Determine whether a probability distribution is given and two reasons why or why not. $\begin{array} { | c | c | } \hline \begin{array} { c } \text { Contributes Most } \\\text { to Happiness }\end{array} & \boldsymbol { P } ( \boldsymbol { x } ) \\\hline \text { Family } & 0.77 \\\text { Friends } & 0.15 \\\text { Work/Study } & 0.08 \\\text { Leisure } & 0.08 \\\text { Music } & 0.06 \\\text { Sports } & 0.04 \\\hline\end{array}$

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Not a probability distribution...

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Question 33

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Use the Poisson model to approximate the probability. Round your answer to four decimal places. -The rate of defects among CD players of a certain brand is 1.5%. Use the Poisson approximation to the binomial distribution to find the probability that among 430 such CD players received by a store, there are exactly three Defective CD players.

Describe the differences in the Poisson and the binomial distribution.

In the month preceding this day, the author's mother made 18 phone calls in 30 days. No calls were made on 17 days, 1 call was made on 8 days, and 2 calls were made on 5 days. Use the Poisson distribution to find the probability of no calls in a day. Based on this probability, how many of the 30 days are expected to have no calls?

A police department reports that the probabilities that 0, 1, 2, 3, and 4 car thefts will be reported in a given day are 0.122, 0.257, 0.270, 0.189, and 0.099, respectively.

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -Choosing 4 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time without replacement, keeping track of the number of red marbles chosen.

Provide an appropriate response. -A 28-year-old man pays $181 for a one-year life insurance policy with coverage of $150,000. If the probability that he will live through the year is 0.9994, what is the expected value for the insurance policy?

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -Choosing 8 marbles from a box of 40 marbles (20 purple, 12 red, and 8 green) one at a time with replacement, keeping track of the number of red marbles chosen.

Provide an appropriate response. Round to the nearest hundredth. -A police department reports that the probabilities that 0, 1, 2, and 3 burglaries will be reported in a given day are 0.46, 0.41, 0.09, and 0.04, respectively. Find the standard deviation for the probability distribution. Round Answer to the nearest hundredth.

State the requirements to use the Poisson distribution as an approximation to the binomial distribution, including the mean for the Poisson distribution as an approximation to the binomial.

Solve the problem. -The probability of winning a certain lottery is $\frac { 1 } { 70,422 }$ . For people who play 545 times, find the mean number of wins.

A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test? Round to three Decimal places.

Solve the problem. -A company manufactures batteries in batches of 6 and there is a 3% rate of defects. Find the mean number of defects per batch.

Use the Poisson model to approximate the probability. Round your answer to four decimal places. -The probability that a call received by a certain switchboard will be a wrong number is 0.02. Use the Poisson distribution to approximate the probability that among 150 calls received by the switchboard, there are at least Two wrong numbers.

Assume that a procedure yields a binomial distribution with a trial repeated $n = 30$ times. Use the binomial probability formula to find the probability of $x = 5$ successes given the probability $p = 1 / 5$ of success on a single trial. Round to three decimal places.

Solve the problem. -On a multiple choice test with 29 questions, each question has four possible answers, one of which is correct. For students who guess at all answers, find the standard deviation for the number of correct answers.

The braking time of a car. Identify the given random variable as being discrete or continuous.

The pH level in a shampoo

Find the indicated probability. Round to three decimal places. -Find the probability of at least 2 girls in 6 births. Assume that male and female births are equally likely and that the births are independent events.