Concept explainers
Finance: European Growth Fund A European growth mutual fund specialize in Mucks from the British Isles, continental Europe. and Scandinavia. The fund has over 100 stocks. Let a be a random variable that represents the monthly percentage return for this fund. Based on information from Morning star (see Problem 19), x has
(a) Let's consider the monthly return of the Mocks in the European growth fund to be a sample from the population of monthly returns of all European stocks. Is it reasonable to assume that a (the average monthly return on the 100 Mocks in the European growth fund) has a distribution that is approximately normal? Explain. Hint. See Problem 19, part (a).
(b) After 9 months, what is the
(c) After 18 months, what is the probability that the average monthly percentage return
(d) Compare your answers to pans (b) and (c) Did the probability increase as n (number of months) increased? Why would this happen?
(c) Interpretation If after IK months the average monthly percentage return
(a)
Whether thex has an approximately normal distribution.
Answer to Problem 20P
Solution:
By central limit theorem we can assume that x has an approximately normal distribution.
Explanation of Solution
Let xbe a random variable that represents the monthly percentage return for a European growth mutual fund with
Since, xrepresent a sample average return based on a large (
(b)
To find: The probability that the average monthly percentage return
Answer to Problem 20P
Solution: After 9 months, the probability that the average monthly percentage return
Explanation of Solution
Let x has a distribution that is approximately normal with
The sample size is n = 9, the sampling distribution for
We convert the interval
Using Table 3 from the Appendix to find the
Hence, the required probability is 0.921.
(c)
To find: The probability that
Answer to Problem 20P
Solution: The probability that
Explanation of Solution
The sampling distribution for
Sample size,
We convert the interval
Using Table 3 from the Appendix to find the
Hence, the required probability is 0.9823.
(d)
To explain: Whether the probability increase as n (number of months) increased.
Answer to Problem 20P
Solution:
Yes, the standard deviation decreases as the sample size increases.
Explanation of Solution
The probability that
The probability is increased as sample sizenincreases, because as we increase the number of months (n), the standard deviation decreases and the probability increased.
(e)
Whether the European stock market might be heating up.
Answer to Problem 20P
Solution:
It is very unlikelyto have mean percentage return of
Explanation of Solution
The sampling distribution for
Sample size,
We convert the interval
This means that the probability of the mean monthly return being above 2% after 18 months is 0.07%. This should be enough to shake our confidence in the statement that
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Chapter 7 Solutions
Understanding Basic Statistics
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