1215

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(91.8 < X < 108.3).

C) P(90.2 < X < 109.8).

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

1215

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

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

B) Kurtosis is equal to 3.

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

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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).

1215

The lower limit of a normal distribution is:

A) negative one.

B) zero.

C) negative infinity.

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

1215

A client will move his investment account unless the portfolio manager earns at least a 10% rate of return on his account. The rate of return for the portfolio that the portfolio manager has chosen has a normal probability distribution with an expected return of 19% and a standard deviation of 4.5%. What is the probability that the portfolio manager will keep this account?

A) 0.950.

B) 0.977.

C) 0.750.

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Since we are only concerned with values that are below a 10% return this is a 1 tailed test to the left of the mean on the normal curve. With μ = 19 and σ = 4.5, P(X ≥ 10) = P(X ≥ μ ? 2σ) therefore looking up -2 on the cumulative Z table gives us a value of 0.0228, meaning that (1 ? 0.0228) = 97.72% of the area under the normal curve is above a Z score of -2. Since the Z score of -2 corresponds with the lower level 10% rate of return of the portfolio this means that there is a 97.72% probability that the portfolio will earn at least a 10% rate of return.