Chapter 2 AP Statistics

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Answer explanation

e. The percentile tells what percent of scores are at or below Pete’s score.

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Answer explanation

d. The normal curve approaches the horizontal axis on the upper side of the graph around the value of 11. This value, which represents 3 standard deviations above the mean is 9 units above the mean of 2. Since 3 standard deviations = 9 units, then 1 standard deviation = 3 units.

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Answer explanation

B. About 20% consume fewer than 4 ounces and about 60% consume fewer than 8 ounces, so about 40% consume between 4 and 8 ounces.

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Answer explanation

A. Solve the following equation for σ: 1.04 = (60-55)/σ. The value 1.04 is the approximate 85th percentile of the standard Normal distribution as found in Table A.

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Is this a probability distribution?

• No

• Yes

Is this a probability distribution?

• No, the sum of p(x) does not equal 1.

• Yes, all p(x) are between 0 and 1.

• No, all p(x) are not between 0 and 1.

• Yes, the sum p(x) is 1.

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Answer explanation

e. The total area under any density curve is 1.

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Answer explanation

c. Two feet constitutes 24 inches. Since there is a variability of about 6 standard deviations in a length that encompasses 99.7% of all observations, we would estimate the standard deviation to be 24/ 4 = 6 inches.

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Answer explanation

d. The distribution of z-scores will have the same shape as the original distribution with a mean of 0 and a standard deviation of 1.