Question

2. The price-earnings ratios of a sample of stocks have a mean value of 13.5 and a standard deviation of 2. If the ratios have a bell-shaped distribution, what can we say about the proportion of ratios that fall between 11.5 and 15.5? a. The interval contains approximately 68% of the ratios. b. The interval contains approximately 95% of the ratios. c. The interval contains approximately 99.7% of the ratios. d. The interval contains approximately 5% of the ratios. e. The interval contains approximately 2.5% of the ratios.

Answer 1

µ = 13.5, σ = 2

The empirical rule states that for a normal distribution:

68% of the data will fall within one standard deviation of the mean.

95% of the data will fall within two standard deviations of the mean.

Almost all (99.7%) of the data will fall within three standard deviations of the mean.

z score for 11.5, z = (X-µ)/σ = (11.5-13.5)/2 = -1

z score for 15.5, z = (X-µ)/σ = (15.5-13.5)/2 = 1

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Answer: a. The interval contains approximately 68% of the ratios.