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Exam 5: Continuous Random Variables and Probability Distributions

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Question 121

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Consider a random sample of size n =1800 from a binomial probability distribution with P = 0.40,and X = number of successes. -Find the mean and standard deviation of the number of successes.

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Mean = E(X)= μ = nP ...

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Question 122

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THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The average amount of time between a score by either team in college soccer games is 15.2 minutes.Suppose that the time between scores follows an exponential distribution. -What is the probability that a soccer game goes for 45 minutes without either team scoring?

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E(T)=1/λ = 15.2,then...

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Question 123

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

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The amount of time you have to wait at a particular stoplight is uniformly distributed between zero and two minutes. -What is the probability that you have to wait more than 30 seconds for the stoplight?

Normal probability plots provide a way to test the assumption that the normal distribution is a close approximation to the actual unknown distribution that supplied the data we are analyzing.

Given a normal random variable X with mean of 70 and standard deviation of 12,the value of the standard normal random variable Z associated with X = 82 is larger than zero.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A random variable X is normally distributed with mean of 50 and variance of 50,and a random variable Y is normally distributed with mean of 100 and variance of 200. -Given the random variables X and Y have a correlation coefficient equal to 0.50,find the mean and variance of the random variable W = 4X+3Y.

One normal distribution has a mean of 5 and a standard deviation of 2.A second normal distribution has a mean of 6 and a standard deviation of 1.Which of the following statements is true?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The amount of time you have to wait at a particular stoplight is uniformly distributed between zero and two minutes. -What is the probability that you have to wait between 15 and 45 seconds for the stoplight?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A wire-spinning machine will spin,on average,12.3 miles before needing maintenance.Assume the time between maintenance is exponentially distributed. -What is the probability that a spinning machine just placed back in service will need maintenance before it produces 4 miles of wire?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A random variable X is normally distributed with mean of 50 and variance of 50,and a random variable Y is normally distributed with mean of 100 and variance of 200. -Given the random variables X and Y have a correlation coefficient equal to -0.50,find the mean and variance of the random variable W = 4X - 3Y.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A random variable X is normally distributed with mean of 50 and variance of 50,and a random variable Y is normally distributed with mean of 100 and variance of 200. -Given the random variables X and Y have a correlation coefficient equal to 0.50,find the mean and variance of the random variable W = 4X - 3Y.

The standardized normal distribution has a mean = 0 and a standard deviation = 10.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A random variable X is normally distributed with mean of 50 and variance of 50,and a random variable Y is normally distributed with mean of 100 and variance of 200. -Given the random variables X and Y have a correlation coefficient equal to -0.50,find the mean and variance of the random variable W = 4X + 3Y.

A two-dimensional plot of the observed data values on the vertical-axis with their corresponding quartile values from a standardized normal distribution on the horizontal-axis is referred to as a:

Sales at a local plumbing wholesaler consist of both over-the-counter sales as well as deliveries.During the course of a month,over-the-counter sales have a mean of $102,972 with a standard deviation of $13,523.Over the same time period,deliveries average $242,354 with a standard deviation of $24,956.Assuming that the sales over-the-counter are independent of deliveries,what are the mean and standard deviation of the wholesaler monthly sales?

Suppose the likelihood that someone who logs onto a particular site on the Internet will purchase an item is 0.10.If the site has 200 people accessing it in the next day,what is the probability that less than 24 customers will make a purchase?

Which type of random variables are used to model market values of various stock prices,production and sales patterns,and studies of import and export behavior?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The amount of time you have to wait at a particular stoplight is uniformly distributed between zero and two minutes. -The median score for the final exam in a chemistry class was 75 and 18% of the students received a grade greater than 80.If the test scores were normally distributed,what is the probability that a randomly selected exam had a score between 75 and 80?