Exam 7: Continuous Probability Distributions

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In a uniform probability distribution, P(x) is constant between the distribution's minimum and maximum values.

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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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The standard deviation of any uniform probability distribution is

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A binomial distribution has 50 trials (n = 50) with a probability of success of 0.50 ( π\pi =0.50). We would like to find the probability of 34 or more successes using the normal distribution to approximate the binomial. Applying the continuity correction factor, what z-score should be used?

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

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A study conducted by a local tennis center revealed that 25 percent of its new members have novice level tennis skills. A membership drive in a metropolitan area resulted in 500 new members. It has been suggested that the normal approximation to the binomial be used to calculate various probabilities. In this problem, can the normal approximation to the binomial be applied? Explain.

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Describe the uniform distribution.

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A study conducted by a local tennis center revealed that 25 percent of its new members have novice level tennis skills. A membership drive in a metropolitan area resulted in 500 new members. What is the probability that 150 or more of the new members are novice tennis players?

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The weekly mean income of a group of executives is $1000 and the standard deviation of this group is $100. The distribution is normal. What percent of the executives have an income of $925 or less?

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The shape of any uniform probability distribution is

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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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The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the mean?

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After arriving at the university student medical clinic, the waiting times to receive service after checking-in follow an exponential distribution with a mean of 10 minutes. Calculate the probability a student waits less than 6 minutes.

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The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. Assuming a normal distribution, what is the probability that a student scored greater than 65?

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For a standard normal distribution, what is the probability that z is greater than 1.75?

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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 is the average monthly amount charged? _______

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In a standard normal distribution, µ = ______ and σ\sigma = _____.

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What proportion of the area under a normal curve is to the right of a z-score of zero? _________

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For the exponential distribution, the mean and standard deviation are equal.

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What is the purpose of using the continuity correction factor when approximating the binomial distribution with a normal distribution?

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