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Exam 6: The Normal Probability Distribution

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Question 71

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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.

A) (i) , (ii) and (iii) are all correct statements
B) (i) is a correct statement but not (ii) or (iii) .
C) (i) and, (iii) are correct statements but not (ii) .
D) (ii) and, (iii) are correct statements but not (i) .
E) All statements are false

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Question 72

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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.

A) (i) , (ii) and (iii) are all correct statements
B) (i) is a correct statement but not (ii) or (iii) .
C) (i) and, (iii) are correct statements but not (ii) .
D) (i) and, (ii) are correct statements but not (iii) .
E) All statements are false

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Question 73

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The total area of a normal probability distribution is

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?

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 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?

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?

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.

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?