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Exam 6: Random Variables and Discrete Probability Distributions

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Number of Horses The random variable X represents the number of horses per family in a rural area in Iowa, with the probability distribution: p ( x )= 0.05 x , x = 2, 3, 4, 5, or 6. {Number of Horses Narrative} Find the variance and standard deviation of X .

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s ² = 1.75,...

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The amount of time that a microcomputer is used per week is an example of a(n)____________________ random variable.

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If X has a binomial distribution with n = 4 and p = 0.3, find P ( X > 1).

The number of accidents that occur annually on a busy stretch of highway is an example of:

The ____________________ of a Poisson distribution is the rate at which successes occur for a given period of time or interval of space.

The mean of a discrete probability distribution for X is the sum of all possible values of X , divided by the number of possible values of X .

Which of the following about the binomial distribution is not a true statement?

If X is a binomial random variable with n = 25, and p = 0.25, then P ( X = 25)= 1.0.

Montana Highways A recent survey in Montana revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 70 miles per hour, were exceeding the limit. Suppose you randomly record the speeds of ten vehicles traveling on US 131 where the speed limit is 70 miles per hour. Let X denote the number of vehicles that were exceeding the limit. {Montana Highways Narrative} Find P (3 £ X £ 6).

Montana Highways A recent survey in Montana revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 70 miles per hour, were exceeding the limit. Suppose you randomly record the speeds of ten vehicles traveling on US 131 where the speed limit is 70 miles per hour. Let X denote the number of vehicles that were exceeding the limit. {Montana Highways Narrative} Find P (4 X

The expected number of heads in 250 tosses of an unbiased coin is 125.

The variance of a binomial distribution for which n = 50 and p = 0.20 is 8.0.

Unsafe Levels of Radioactivity The number of incidents at a nuclear power plant has a Poisson distribution with a mean of 6 incidents per year. {Unsafe Levels of Radioactivity Narrative} Find the variance of the number of incidents in one year.

A(n)____________________ random variable is one whose values are uncountable.

911 Phone Calls 911 phone calls arrive at the rate of 30 per hour at the local call center. {911 Phone Calls Narrative} If no calls are currently being processed, what is the probability that the desk employee can take four minutes break without being interrupted?

Which of the following is a discrete random variable?

Classified Department Phone Calls A classified department receives an average of 10 telephone calls each afternoon between 2 and 4 P.M. The calls occur randomly and independently of one another. {Classified Department Phone Calls Narrative} Find the probability that the department will receive 13 calls between 2 and 4 P.M. on a particular afternoon.

Given that X is a discrete random variable, then the laws of expected value and variance can be applied to show that E ( X + 5)= E ( X )+ 5, and V ( X + 5)= V ( X )+ 25.

The probability of a failure in a binomial experiment is denoted by ____________________.

Online Bankers An official from the securities commission estimates that 75% of all online bankers have profited from the use of insider information. Assume that 15 online bankers are selected at random from the commission's registry. {Online Bankers Narrative} Find the probability that all 15 have profited from insider information.