Exam 5: Continuous Random Variables and Probability Distributions

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A continuous random variable X has the probability density function: f(x)= 2e-2x,x ≥ 0. -What is the probability that x is between 1 and 3?

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The continuous random variable X is uniformly distributed over the interval 4 to 10. -What is P(5 ≤ X ≤ 11)?

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In using finance models we must be aware that caution and continuous clear observation and thinking cannot be replaced by models developed from past events.

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The probability is 0.99 that a randomly-selected five-pound box of nails contains at least how many nails approximately?

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let the random variable Z follow a standard normal distribution. -What is P(-0.44 < Z < 1.2)?

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During a professor's office hours,students arrive,on average,every ten minutes.Assume that the distribution of the time between arrivals follows an exponential distribution.Suppose that a student has just left. What is the probability that the professor has more than 20 minutes before the next student shows up?

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The number of nails in a five-pound box of nails is normally distributed with a mean of 563.3 and a standard deviation of 33.2. -What is the probability that there are less than 500 nails in a randomly-selected five-pound box of nails?

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let the random variable Z follow a standard normal distribution. -What is P(Z > 1.2)?

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If the random variable Z follows a standard normal distribution,then,σz = If the random variable Z follows a standard normal distribution,then,σ<sub>z</sub> =    . .

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A professor sees students during regular office hours.Times spent with students follow an exponential distribution with mean of 12 minutes. -Find the probability that a given student spends more than 8 minutes with the professor.

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Given that Z is a standard normal variable,the value z1 for which P(Z ≤ z1)= 0.242 is:

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________ is the continuous probability distribution used most often for economics and business applications.

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A very large logging operation has serious problems keeping their skidders operating properly.The equipment fails at the rate of 3 breakdowns every 48 hours.Assume that x is time between breakdowns and is exponentially distributed.The probability of a single breakdown within 24 hours is:

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The standard normal distribution is the most well-known discrete distribution in statistics.

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The distribution of IQ scores for high school graduates is normally distributed with mean μ = 104 and standard deviation σ = 16. -What fraction of the IQ scores would be between 97 and 126?

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Let the random variable Z follow a standard normal distribution,and let z1 be a possible value of Z that is unknown but identifiable by position and area.Find z1 if the area to the right of z1 is 0.8413.

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A continuous random variable X has the probability density function: f(x)= 2e-2x,x ≥ 0. -What is the distribution of the random variable X?

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The stamping machine on a production line periodically is taken off-line for maintenance.Assume that the amount of time the machine is off-line is uniformly distributed between 15 and 30 minutes. -What is the probability that the machine is off-line for more than 18 minutes?

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If the random variable Y = a + bX,then μY = a + bμX.

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Let the random variable X follow a normal distribution with mean μ = 48 and variance σ2 = 60.84. -Find the probability that X is greater than 36 and less than 60.

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