Exam 6: Continuous Random Variables

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The standardized normal quartile value Oi is the z value that gives an area of i/(n - 1)to its right under the normal curve.

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The time between breakdowns of an alarm system is exponentially distributed with mean 10 days.What is the probability that there are no breakdowns on a given day?

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The specific shape of each normal distribution is determined by its ____________ and ____________.

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The random variable x has a uniform distribution when x lies between the values of 4 and 10.When x = 10,what is the value of f(x)?

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Suppose that the waiting time for a license plate renewal at a local office of a state motor vehicle department has been found to be normally distributed with a mean of 30 minutes and a standard deviation of 8 minutes.What is the probability that a randomly selected individual will have a waiting time of no more than 22 minutes

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Given that the length an athlete throws a hammer is a normal random variable with mean 50 feet and standard deviation 5 feet,what is the probability he throws it between 50 feet and 60 feet?

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The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches.What is the probability that a sheet selected at random will be less than 29.75 inches long?

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The actual weight of hamburger patties is an example of a continuous random variable.

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When a ____________ probability distribution is used to approximate a ____________ probability distribution,we must make a ____________ correction.

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An aptitude test has a mean score of 80 and a standard deviation of 5.The population of scores is normally distributed.What raw score corresponds to the 70th percentile?

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If the mileage per gallon for a car is normally distributed,32 mpg has a z score of 1.2,and 24 mpg has a z score of -.4,what is the mean mpg of the distribution?

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An apple juice producer buys all his apples from a conglomerate of apple growers in one northwestern state.The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce.What is the probability that a randomly selected apple will contain between 2.00 and 3.00 ounces?

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While conducting experiments,a marine biologist selects water depths from a uniformly distributed collection that vary between 2.00 m and 7.00 m.What is the expected value of the water depth?

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The cashier service time at the local branch of the Rivertown bank has an exponential distribution with a mean of 2.5 minutes.What is the probability that the service time exceeds 3 minutes?

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The mean of a standard normal distribution is always equal to 1.

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Suppose that the times required for a cable company to fix cable problems in its customers' homes are uniformly distributed between 40 minutes and 65 minutes.What is the probability that a randomly selected cable repair visit falls within 2 standard deviations of the mean?

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The binomial random variable x consists of n = 60 trials and has the probability of failure q = 0.4.Using the normal approximation,compute the probability of 19 successes.

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Find z when the area to the left of z is .05.

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A standard normal distribution has a mean of ____________ and standard deviation of ____________.

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Consider a normal population with a mean of 10 and a variance of 4.Find P(X > 7).

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