Exam 7: Continuous Probability Distributions

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Asymptotic means that the normal curve gets closer and closer to the X-axis but never actually touches it.

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What is the formula to convert any normal distribution to the standard normal distribution? _______________________

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z = (X - μ\mu )/ σ\sigma

One of the properties of the normal curve is that it gets closer to the horizontal axis,but never touches it.What is this property of the normal curve called? _________________

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Asymptotic

Some normal probability distributions have equal arithmetic means,but their standard deviations may be different.

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An accelerated life test on a large number of type-D alkaline batteries revealed that the mean life for a particular use before they failed is 19.0 hours.The distribution of the lives approximated a normal distribution.The standard deviation of the distribution was 1.2 hours.About 95.44 percent of the batteries failed between what two values?

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What does a z value of -2.00 indicate about the corresponding X value? _______________________

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Suppose a tire manufacturer wants to set a mileage guarantee on its new XB 70 tire.Tests revealed that the tire's mileage is normally distributed with a mean of 47,900 miles and a standard deviation of 2,050 miles.The manufacturer wants to set the guaranteed mileage so that no more than 5 percent of the tires will have to be replaced.What guaranteed mileage should the manufacturer announce?

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The area under the normal curve within plus and minus one standard deviation of the mean is about 68.26%.

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Some normal probability distributions have different arithmetic means and different standard deviations.

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For a uniform probability distribution,the probability of any event is equal to 1/(b-a).

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What is the area under the normal curve between z = 0.0 and z = 2.0?

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A major credit card company has determined that customers charge between $100 and $1100 per month.Given that the average monthly amount charged is uniformly distributed,what percent of monthly charges are equal to $500? __________

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The mean amount of gasoline and services charged by Key Refining Company credit customers is $70 per month.The distribution of amounts spent is approximately normal with a standard deviation of $10.What is the probability of selecting a credit card customer at random and finding the customer charged between $70 and $83?

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The total area under the normal curve is 100%.

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What is the area under the normal curve between z = -1.0 and z = -2.0?

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The total area within any continuous probability distribution is equal to 1.00.

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The Empirical Rule of probability can be applied to the uniform probability distribution.

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What is a normal distribution with a mean of 0 and a standard deviation of 1 called?

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Which of the following is true in a normal distribution?

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What is an important similarity between the uniform and normal probability distributions?

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