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Exam 6: The Normal Probability Distribution

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Question 71

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A financial advising company has determined that the price-to-earnings ratios for 20 randomly selected publicly traded companies range between 0.9 and 2.9. Given that the price-to-earnings ratios are uniformly distributed, what percent of price-to-earnings ratios are between 1.90 and 2.48?

A) 19%
B) 20%
C) 26%
D) 29%
E) None of the choices are correct

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Question 72

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Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years, (based on data from "Getting Things Fixed," Consumer Reports). -If you want to provide a warranty so that only 3% of the TV sets will be replaced before the warranty expires, the length of warranty you would recommend would be _____years.

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Question 73

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i. A z-score is the distance between a selected value (X) and the population mean (μ) divided by the population standard deviation (σ) . Ii) The standard normal distribution is a special normal distribution with a mean of 0 and a standard deviation of 1. Iii) A computed z for X values to the right of the mean is negative.

The mean score of a college entrance test is 500; the standard deviation is 75. The scores are normally distributed. What percent of the students scored below 320?

The total area of a normal probability distribution is

Ball-Bearings, Inc. produces ball bearings automatically on a Kronar BBX machine. For one of the ball bearings, the mean diameter is set at 20.00 mm (millimetres) . The standard deviation of the production over a long period of time was computed to be 0.150 mm. What percent of the ball bearings will have diameters 20.27 mm or more?

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?

A sample of 500 evening students revealed that their annual incomes were normally distributed with a mean income of $50,000 and a standard deviation of $4,000. How many students earned between $45,000 and $53,000?

i. Asymptotic means that the normal curve gets closer and closer to the X-axis but never actually touches it. Ii) When referring to the normal probability function, there is not just one of them; there is a "family" of them. Iii) Some normal probability distributions have equal arithmetic means, but their standard deviations may be different.