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Exam 5: Probability Distributions

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Question 51

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An airline estimates that 98% of people booked on their flights actually show up. If the airline books 76 people on a flight for which the maximum number is 74, what is the probability that the number of people who show up will exceed the capacity of the plane?

A) 0.8051
B) 0.3340
C) 0.2154
D) 0.5494

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Question 52

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Solve the problem. -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. $\begin{array} { c | c } \mathrm { x } & \mathrm { P } ( \mathrm { x } ) \\\hline 0 & 0.1296 \\\hline 1 & 0.3456 \\\hline 2 & 0.3456 \\\hline 3 & 0.1536 \\\hline 4 & 0.0256\end{array}$

A) 0.96
B) 1.12
C) 1.88
D) 0.98

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Question 53

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Determine whether the given procedure results in a binomial distribution. If not, state the reason why. - $\rho = \frac { 1 } { 6 }$ n = 6, x = 3,

Answer the question. -Spinning a roulette wheel 3 times, keeping track of the winning numbers.

Use the normal distribution to approximate the desired probability. -Find the probability of selecting exactly 8 girls.

In a certain college, 33% of the physics majors belong to ethnic minorities. If 10 students are selected at random from the physics majors, that is the probability that no more than 6 belong to an ethnic minority?

Provide an appropriate response. -Identify each of the variables in the Binomial Probability Formula. $P ( x ) = \frac { n ! } { ( n - x ) ! x ! } \cdot p ^ { x } \cdot q ^ { n - x }$ Also, explain what the fraction $\frac { n ! } { ( n - x ) ! x ! }$ computes.

Assume that a probability distribution is described by the discrete random variable x that can assume the values 1, 2, . . . , n; and those values are equally likely. This probability has mean and standard deviation described as follows: $\mu = \frac { \mathrm { n } + 1 } { 2 } \text { and } \sigma = \sqrt { \frac { \mathrm { n } ^ { 2 } - 1 } { 12 } }$ Show that the formulas hold for the case of n = 7.

Solve the problem. -Find the variance for the given probability distribution. $\begin{array} { c | c } \mathrm { x } & \mathrm { P } ( \mathrm { x } ) \\\hline 0 & 0.17 \\\hline 1 & 0.28 \\\hline 2 & 0.05 \\\hline 3 & 0.15 \\\hline 4 & 0.35\end{array}$

Provide an appropriate response. -Sampling without replacement involves dependent events, so this would not be considered a binomial experiment. Explain the circumstances under which sampling without replacement could be considered independent and, thus, binomial.

Use the given values of n and p to find the minimum usual value µ - 2? and the maximum usual value µ + 2? - $n = 604 , p = \frac { 4 } { 7 }$

Determine whether the given procedure results in a binomial distribution. If not, state the reason why. - $n = 4 , x = 3 , p = \frac { 1 } { 6 }$

Suppose that computer literacy among people ages 40 and older is being studied and that the accompanying tables describes the probability distribution for four randomly selected people, where x is the number that are computer literate. Is it unusual to find four computer literates among four randomly selected people? $\begin{array} { c | c } x & P ( x ) \\\hline 0 & 0.16 \\\hline 1 & 0.25 \\\hline 2 & 0.36 \\\hline 3 & 0.15 \\\hline 4 & 0.08\end{array}$

Identify the given random variable -The number of oil spills occurring off the Alaskan coast

Solve the problem. -The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.4521, 0.3970, 0.1307, 0.0191, and 0.0010, respectively. Find the variance for the probability distribution.

Provide an appropriate response. -List the two requirements for a probability histogram. Discuss the relationship between the sum of the probabilities in a probability distribution and the total area represented by the bars in a probability histogram.

Determine whether the following is a probability distribution. If not, identify the requirement that is not satisfied. -If a person is randomly selected from a certain town, the probability distribution for the number, x, of siblings is as described in the accompanying table. $\begin{array} { c | c } \mathrm { x } & \mathrm { P } ( \mathrm { x } ) \\\hline 0 & 0.27 \\1 & 0.29 \\2 & 0.23 \\3 & 0.10 \\4 & 0.08 \\5 & 0.02\end{array}$

A test consists of 10 true/false questions. To pass the test a student must answer at least 7 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?

Solve the problem. -A 28-year-old man pays $57 for a one-year life insurance policy with coverage of $100,000. If the probability that he will live through the year is 0.9992, what is the expected value for the insurance policy?

Use the normal distribution to approximate the desired probability. -Find the probability of selecting 12 or more girls.