Exam 5: Probability: an Introduction to Modeling Uncertainty

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Consider a random experiment of rolling 2 dice. The sample space for rolling two dice is shown. Let S be the set of all ordered pairs listed in the figure. What is probability of rolling a sum larger than 10?

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A bucket contains 3 red balls, 4 yellow balls, and 5 purple balls. One ball is taken from the bucket and is not replaced. Another ball is taken from the bucket. What is the probability that the first ball is red and the second ball is purple?

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In a binomial​ experiment, what does it mean to say that each trial is independent of the other​ trials?

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Given that A and B are independent with P(A ∪ B) = 0.8 and P(Bc) = 0.3, find P(A).

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What is the mean of x, given the exponential probability function f(x)=120ex20 for x0 ? f ( x ) = \frac { 1 } { 20 } e ^ { \frac { x } { 20 } } \text { for } x \geq 0 \text { ? }

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The newest model of smart car is supposed to get excellent gas mileage. A thorough study showed that gas mileage (measured in miles per gallon) is normally distributed with a mean of 75 miles per gallon and a standard deviation of 10 miles per gallon. What value represents the 50th percentile of this distribution? ​​

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Two events are independent if

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An initial estimate of the probabilities of events is a ______________ probability.

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The cross tabulation shown below shows employees of a communications company classified by age and field of expertise. What is the probability that a randomly selected engineer is under the age of 35? ​ Under - + Total Engineering 8,399 8,663 7,072 Business 14,515 14,988 26,683 Education 6,738 5,657 8,669 Liberal Arts 11,415 11,484 12,111 Total ​

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The random variable X is normally distributed with mean of 80 and standard deviation of 10. What is the probability that a value of X chosen at random will be between 70 and 90? ​

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A nickel and a dime are tossed. We are interested only in the event that includes at least one head appears on a single toss of both coins. What are the possible outcomes?

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Probability is​ the

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An experiment consists of determining the speed of automobiles on a highway by the use of radar equipment. The random variable in this experiment is a

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The _______________ probability distribution can be used to estimate the number of vehicles that go through an intersection during the lunch hour. ​​

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A bucket contains 3 red balls, 4 yellow balls, and 5 purple balls. One ball is taken from the bucket and is not replaced. Another ball is taken from the bucket. Are the events of pulling first ball is red then a purple one independent or dependent?

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Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive thru. It was discovered that The time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the probability that it takes less than one minute to fill an order?

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Consider a random experiment of rolling 2 dice. The sample space for rolling two dice is shown. Let S be the set of all ordered pairs listed in the figure. What are the possible outcomes for the event of rolling a 7?

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If a​ z-score is​ zero, then the corresponding x-value must be equal to the ​​

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The random variable X is known to be uniformly distributed between 2 and 12. Compute E(X), the expected value of the distribution.

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Which statement is true about mutually exclusive events?

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