Determine whether the given procedure results in a binomial distribution. If not, state the reason why.

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1 Math 5.3 Binomial Probability Distributions Name 1) Binomial Distrbution: Determine whether the given procedure results in a binomial distribution. If not, state the reason why. 2) Rolling a single die 26 times, keeping track of the numbers that are rolled. A) Not binomial: the trials are not independent. B) Procedure results in a binomial distribution. C) Not binomial: there are too many trials. D) Not binomial: there are more than two outcomes for each trial. 3) Rolling a single die 53 times, keeping track of the "fives" rolled. A) Not binomial: the trials are not independent. B) Not binomial: there are more than two outcomes for each trial. C) Not binomial: there are too many trials. D) Procedure results in a binomial distribution. 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. 4) n = 4, x = 3, p = 1 6 A) B) C) D)

2 Find the indicated probability. Round to three decimal places. 5) 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? A) B) C) D) ) 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. A) B) C) D) Find the indicated probability. 7) The brand name of a certain chain of coffee shops has a 46% recognition rate in the town of Coffleton. An executive from the company wants to verify the recognition rate as the company is interested in opening a coffee shop in the town. He selects a random sample of 8 Coffleton residents. Find the probability that exactly 4 of the 8 Coffleton residents recognize the brand name. A) B) C) D) ) In a survey of 300 college graduates, 56% reported that they entered a profession closely related to their college major. If 8 of those survey subjects are randomly selected without replacement for a follow-up survey, what is the probability that 3 of them entered a profession closely related to their college major? A) B) C) D)

3 Math 227 Sec 5.4 Parameters for Binomial Distributions Name 1) Parameters For Binomial Distributions 2) Range Rule of Thumb Find the mean, µ, for the binomial distribution which has the stated values of n and p. Round answer to the nearest tenth. 3) n = 38; p = 0.2 A) µ = 7.9 B) µ = 8.3 C) µ = 7.6 D) µ = 7.1 Find the standard deviation,, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth. 4) n = 29; p = 0.2 A) = 2.15 B) = 5.42 C) = 6.27 D) = Use the given values of n and p to find the minimum usual value µ - 2 and the maximum usual value µ + 2. Round your answer to the nearest hundredth unless otherwise noted. 5) n = 93, p = 0.24 A) Minimum: 14.08; maximum: B) Minimum: 18.2; maximum: C) Minimum: 30.56; maximum: D) Minimum: ; maximum:

4 6) n = 237, p = 1 4 A) Minimum: 52.58; maximum: B) Minimum: 72.58; maximum: C) Minimum: 45.92; maximum: D) Minimum: 49.82; maximum: Solve the problem. 7) 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. A) 2.8 B) 4.0 C) 3.5 D) 0.2 8) 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. A) 3 B) 2.25 C) 7.5 D) 1.5 9) According to a college survey, 22% of all students work full time. Find the standard deviation for the number of students who work full time in samples of size 16. A) 3.5 B) 1.9 C) 1.7 D) 2.6 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 ) 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? A) Yes B) No 11) 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 530 consumers who recognize the Dull Computer Company name? A) Yes B) No 2

5 Math 227 Sec 5.5 Poisson Probability Distributions Name 1) Poisson Distribution 2) Formula of Poisson Probability Distribution 3) Requirements for the Poisson Distribution 4) Paramenters of the Poisson Distribution 1

6 Use the Poisson Distribution to find the indicated probability. 5) If the random variable x has a Poisson Distribution with mean µ = 3, find the probability that x = 5. A) B) C) D) Find the indicated mean. 6) The mean number of homicides per year in one city is Suppose a Poisson distribution will be used to find the probability that on a given day there will be fewer than 4 homicides. Find the mean of the appropriate Poisson distribution (the mean number of homicides per day). Round your answer to four decimal places. A) 5.35 B) C) D) ) A certain rare form of cancer occurs in 37 children in a million, so its probability is In the city of Normalville there are 74,090,000 children. A Poisson distribution will be used to approximate the probability that the number of cases of the disease in Normalville children is more than 2. Find the mean of the appropriate Poisson distribution (the mean number of cases in groups of 74,090,000 children). A) B) 27,400 C) 274 D) 2740 Use the Poisson model to approximate the probability. Round your answer to four decimal places. 8) Suppose the probability of contracting a certain disease is p = for a new case in a given year. Use the Poisson distribution to approximate the probability that in a town of 6000 people there will be at least one new case of the disease next year. A) B) C) D) E)

MATH 227 CP 6 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

MATH 227 CP 6 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Identify the given random variable as being discrete or continuous. 1) The number of phone