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The Vanguard Balanced Index Fund seeks to maintain an allocation of 60% to stocks and 40% to bonds. With low fees and a consistent investment approach, this fund ranks fourth out of 792 funds that allocate 50% to 70% to stocks (US News, March 2017). Based on historical data, the expected return and standard deviation of this fund is estimated as 7.49% and 6.41%, respectively. Assume that the fund returns are stable and are normally distributed. a) What is the probability that the fund will generate a return between 5% and 10%? b) What is the lowest return of the fund that will place it in the top 10% (90th percentile) of the distribution?
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Suppose we know that the ages of employees in Industries A, B, and C are normally distributed. We are given the following information on the relevant parameters: Graphically compare the ages of employees in Industry A with Industry B. Repeat the comparison for Industry A with Industry C.
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WHAT IS THE STANDARD NORMAL DISTRIBUTION?
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Find the following probabilities for the standard normal random variable Z. P(0 ≤ Z ≤ 1.96) P(−1.52 ≤ Z ≤ 1.96) P(1.52 ≤ Z ≤ 1.96) P(Z > 4)
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For the standard normal variable Z, find the z values that satisfy the following probability statements. P(Z ≤ z) = 0.6808 d. P(Z > z) = 0.0212 P(Z ≤ z) = 0.90 e. P(−z ≤ Z ≤ z) = 0.95 P(Z ≤ z) = 0.0643
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WHAT IS THE STANDARD TRANSFORMATION: CONVERTING X INTO Z?
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Scores on a management aptitude exam are normally distributed with a mean of 72 and a standard deviation of 8. What is the probability that a randomly selected manager will score above 60? What is the probability that a randomly selected manager will score between 68 and 84?
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WHAT IS THE INVERSE TRANSFORMATION: CONVERTING Z INTO X?
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