"quantity"exercise:Mean value of standard error samples
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Questions 1:
An analyst applies four valuation screens to a set of potential investments. The screens are independent of each other.
If there are 1,200 potential investments, the number expected to simultaneously pass all four screens is closest to:
A、 360.
B、 97.
C、 42.
Questions 2:
An analyst gathered the following information about a stock index:
If the analyst takes a sample of 36 companies from the index, the standard error of the sample mean is closest to:
A、 $400,000.
B、 $533,333.
C 、$88,889.
C is correct. As the screens are independent, the probability of passing all four simultaneously is the product of their respective probabilities:
P(ABCD) = P(A)P(B)P(C)P(D) where
P(A) = 0.65 and is the probability of passing valuation screen 1
P(B) = 0.45 and is the probability of passing valuation screen 2
P(C) = 0.40 and is the probability of passing valuation screen 3
P(D) = 0.30 and is the probability of passing valuation screen 4
P(ABCD) = 0.65 × 0.45 × 0.40 × 0.30 = 0.0351.
Given 1,200 potential investments, approximately 1,200 × 0.0351 = 42.12 ~ 42 will pass the screens.
A is incorrect. It uses only the smallest of the given probabilities as in 1,200 × 0.30 = 360.
B is incorrect. It subtracts the given probabilities from 1.00 and uses the product of these values: [(1 – 0.65) × (1 – 0.45) × (1 – 0.40) × (1 – 0.30)] × 1,200 = (0.35 × 0.55 × 0.60 × 0.70) × 1,200 = 0.08085 × 1,200 = 97.02 ~ 97.
B is correct. The standard error of the sample mean is equal to the population standard deviation (σ) divided by the square root of the number of observations in the sample (n):
C is incorrect. It uses the following formula: $3,200,000/36 = $88,889.
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