Exam 5: Discrete Probability Distributions

Find the mean of the given probability distribution. -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. () 0 0.1296 1 0.3456 2 0.3456 3 0.1536 4 0.0256

The probability that a radish seed will germinate is 0.7. A gardener plants seeds in batches of 20. Find the standard deviation for the number of seeds germinating in each 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. - $\mathrm { n } = 1212 , \mathrm { p } = 0.98$

Provide an appropriate response. Round to the nearest hundredth. -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 () 0 0.24 1 0.01 2 0.12 3 0.16 4 0.01 5 0.14 6 0.11 7 0.21

An archer is able to hit the bull's-eye 55% of the time. If she shoots 8 arrows, what is the probability that she gets exactly 4 bull's-eyes? Assume each shot is independent of the others.

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

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -Rolling a single die 36 times, keeping track of the "fives" rolled.

Identify the given random variable as being discrete or continuous. -The pH level in a shampoo

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. - $\mathrm { n } = 336 , \mathrm { p } = 0.257 \text { Round your answers to the nearest thousandth. }$

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. -Rolling a single die 33 times, keeping track of the numbers that are rolled.

In Hannah's school, there are 871 students of which 21% come from single-parent families. Consider the probability that among 80 randomly selected students there are at least 20 that come from single-parent families. Can this probability be found by using the binomial probability formula? Why or why not?

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. - $n = 64 , x = 3 , p = 0.04$

Identify the given random variable as being discrete or continuous. -The height of a randomly selected student

Identify the given random variable as being discrete or continuous. -The number of freshmen in the required course, English 101

The probability of winning a certain lottery is $\frac { 1 } { 76,394 }$ For people who play 987 times, find the mean number of wins.

Focus groups of 13 people are randomly selected to discuss products of the Yummy Company. It is determined that the mean number (per group) who recognize the Yummy brand name is 10.1, and the standard deviation is 0.55. Would it be unusual to randomly select 13 people and find that fewer than 7 recognize the Yummy brand name?

List the three methods for finding binomial probabilities in the table below, and then complete the table to discuss the advantages and disadvantages of each. Methods Advantage Disadvantage

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. - $\mathrm { n } = 269 , \mathrm { p } = \frac { 1 } { 3 }$

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.

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 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 480 jawbreakers that weigh more than .4 ounces?