JustasS

A stock portfolio's returns are normally distributed. It has had a mean annual return of 25% with a standard deviation of 40%. The probability of a return between -41% and 91% is closest to:

A) 90%.

B) 65%.

C) 95%.

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A 90% confidence level includes the range between plus and minus 1.65 standard deviations from the mean. (91 − 25) / 40 = 1.65 and (-41 − 25) / 40 = -1.65.

JustasS

A stock portfolio has had a historical average annual return of 12% and a standard deviation of 20%. The returns are normally distributed. The range –27.2 to 51.2% describes a:

A) 95% confidence interval.

B) 68% confidence interval.

C) 99% confidence interval.

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The upper limit of the range, 51.2%, is (51.2 − 12) = 39.2 / 20 = 1.96 standard deviations above the mean of 12. The lower limit of the range is (12 − (-27.2)) = 39.2 / 20 = 1.96 standard deviations below the mean of 12. A 95% confidence level is defined by a range 1.96 standard deviations above and below the mean.

JustasS

A normal distribution can be completely described by its:

A) skewness and kurtosis.

B) mean and variance.

C) mean and mode.

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The normal distribution can be completely described by its mean and variance.

JustasS

The lower limit of a normal distribution is:

A) negative one.

B) negative infinity.

C) zero.

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By definition, a true normal distribution has a positive probability density function from negative to positive infinity.

JustasS

In a normal distribution, the:

A) mean is less than the mode.

B) mean is greater than the median.

C) median equals the mode.

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In a normal distribution, the mean, median, and mode are all equal.

JustasS

A normal distribution is completely described by its:

A) mean, mode, and skewness.

B) median and mode.

C) variance and mean.

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By definition, a normal distribution is completely described by its mean and variance.

JustasS

Which of the following statements about a normal distribution is least accurate?

A) Approximately 34% of the observations fall within plus or minus one standard deviation of the mean.

B) The distribution is completely described by its mean and variance.

C) Kurtosis is equal to 3.

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Approximately 68% of the observations fall within one standard deviation of the mean. Approximately 34% of the observations fall within the mean plus one standard deviation (or the mean minus one standard deviation).

JustasS

If X has a normal distribution with μ = 100 and σ = 5, then there is approximately a 90% probability that:

A) P(93.4 < X < 106.7).

B) P(90.2 < X < 109.8).

C) P(91.8 < X < 108.3).

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100 +/- 1.65 (5) = 91.75 to 108.25 or P ( P(91.75 < X < 108.25).

JustasS

A random variable follows a continuous uniform distribution over 27 to 89. What is the probability of an outcome between 34 and 38?

A) 0.0645.

B) 0.0546.

C) 0.0719.

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P(34 ≤ X ≤ 38) = (38 − 34) / (89 − 27) = 0.0645

JustasS

Consider a random variable X that follows a continuous uniform distribution: 7 ≤ X ≤ 20. Which of the following statements is least accurate?

A) F(21) = 0.00.

B) F(12 ≤ X ≤ 16) = 0.307.

C) F(10) = 0.23.

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F(21) = 1.00 The probability density function for a continuous uniform distribution is calculated as follows: F(X) = (X – a) / (b – a), where a and b are the upper and lower endpoints, respectively. (If the given X is greater than the upper limit, the probability is 1.0.) Shortcut: If you know the properties of this function, you do not need to do any calculations to check the other choices.
The other choices are true.

• F(10) = (10 – 7) / (20 – 7) = 3 / 13 = 0.23
• F(12 ≤ X ≤ 16) = F(16) – F(12) = [(16 – 7) / (20 – 7)] − [(12 – 7) / (20 – 7)] = 0.692 − 0.385 = 0.307