AP Statistics Chapter 2

The distribution of weekly incomes follows the normal probability distribution, with a mean of $1,000 and a standard deviation of $100. What is the sign of the z value corresponding to an income of $1,200?

• negative

• positive

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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

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

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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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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.

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Answer explanation

b. Using technology: Normalcdf(lower: 2, upper: 1000, mean: 1.45, SD: 0.4) = 0.0846.

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Answer explanation

c. Gina’s z-score is z = (540 - 470)/ 110 = 0.27.

Colleen’s z-score is (530 - 510)/103 = 0.194.