Exam 5: Discrete Probability Distributions

The cost of a randomly selected orange

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 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?

Find the indicated probability. Round to three decimal places. -A machine has 11 identical components which function independently. The probability that a component will fail is 0.2. The machine will stop working if more than three components fail. Find the probability that the Machine will be working.

Solve the problem. -According to a college survey, 22% of all students work full time. Find the mean for the number of students who work full time in samples of size 16.

In a certain town, 30% 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. () 0 0.2401 1 0.4116 2 0.2646 3 0.0756 4 0.0081

Based on a USA Today poll, assume that 10% of the population believes that college is no longer a good investment. Find the probability that among 16 randomly selected people, at least 1 believes that college is no longer a good investment.

Provide an appropriate response. Round to the nearest hundredth. -The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.6274, 0.3102, 0.0575, 0.0047, and 0.0001, respectively. Find the standard deviation for the probability distribution.

Answer the question. -Suppose that weight of adolescents is being studied by a health organization and that the accompanying tables describes the probability distribution for three randomly selected adolescents, where x is the number who are Considered morbidly obese. Is it unusual to have no obese subjects among three randomly selected adolescents? () 0 0.111 1 0.215 2 0.450 3 0.224

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 0.210 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.

Provide an appropriate response. -The binomial distribution applies only to cases involving two types of outcomes, whereas the multinomial distribution involves more than two categories. Suppose we have three types of mutually exclusive outcomes Denoted by A, B, and C $\text { Let } \mathrm { P } ( \mathrm { A } ) = \mathrm { p } _ { 1 } , \mathrm { P } ( \mathrm { B } ) = \mathrm { p } _ { 2 } , \mathrm { P } ( \mathrm { C } ) = \mathrm { p } _ { 3 }$ . In n independent trials, the probability of $\mathrm { X } _ { 1 }$ outcomes of type A, $X 2$ outcomes of type B, and $X3$ outcomes of type C is given by $\frac { \mathrm { n } ! } { \left( \mathrm { x } _ { 1 } \right) ! \left( \mathrm { x } _ { 2 } \right) ! \left( \mathrm { x } _ { 3 } \right) ! } \cdot \mathrm { p } ^ { \mathrm { x } } 1 \cdot \mathrm { p } ^ { \mathrm { x } _ { 2 } } \cdot \mathrm { p } _ { 3 } ^ { \mathrm { x } _ { 3 } }$ A genetics experiment involves four mutually exclusive genotypes identified as A, B, C, and D, and they are all Equally likely. If 10 offspring are tested, find the probability of getting exactly 2 A's,3 B's,3 C's, and 2 D's by Expanding the above expression so that it applies to four types of outcomes instead of only three. Round your Answer to five decimal places.

() 0 0.110 1 0.053 2 -0.052 3 0.168 4 0.111 5 0.610

Use the Poisson Distribution to find the indicated probability. -A naturalist leads whale watch trips every morning in March. The number of whales seen has a Poisson distribution with a mean of 1.9. Find the probability that on a randomly selected trip, the number of whales seen Is 5.

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 $\mu + 2 \sigma$ -The Acme Candy Company claims that 60% of the jawbreakers it produces weigh more than .4 ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be unusual for this sample of 800 to contain 575 jawbreakers that weigh more than .4 ounces?

Solve the problem. -A die is rolled 9 times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos.

Solve the problem. -A company manufactures batteries in batches of 28 and there is a 3% rate of defects. Find the variance for the number of defects per batch.

Describe the Poisson distribution and give an example of a random variable with a Poisson distribution.

Find the standard deviation, $\sigma$ , for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. - $\mathrm { n } = 1680 ; \mathrm { p } = 0.57$

Use the Poisson Distribution to find the indicated probability. -If the random variable x has a Poisson Distribution with mean $\mu = 0.693$ find the probability that x = 4.

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 634 consumers who recognize the Dull Computer Company name?

Solve the problem. -A die is rolled 10 times and the number of twos that come up is tallied. If this experiment is repeated many times, find the standard deviation for the number of twos.