
Finance: Templeton Funds Templeton world is a mutual fund that invests in both U.S. and foreign markets. Let x he a random variable that represents the monthly percentage return for the Templeton World fund. Based on information from the Morningstar Guide to Mutual Funds (available in most libraries), x has
(a) Templeton World fund has over 250 stocks that combine together to give the overall monthly percentage return x. We can consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all world stocks. Then we see that the overall monthly return x for Templeton World fund is itself an average return computed using all 250 stocks in the fund. Why would this indicate that x has an approximately
(b) After 6 months, what is the
(c) After 2 years, what is the probability that
(d) Compare your answers to parts (b) and (c). Did the probability increase as n (number of months) increased? Why would this happen ?
(e)Interpretation If after 2 years the average monthly percentage return
(a)

Whether the x has an approximately normal distribution.
Answer to Problem 19P
Solution:
By central limit theorem we can assume that x has an approximately normal distribution.
Explanation of Solution
Let x be a random variable that represents the monthly percentage return for a European growth mutual fund with
Since, x itself represent a sample average return based on a large (
(b)

To find: The probability that the average monthly percentage return
Answer to Problem 19P
Solution: After 6 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 = 6, the sampling distribution for
We convert the interval
Using Table 3 from the Appendix to find the
Hence, the required probability is 0.8105.
(c)

To find: The probability that
Answer to Problem 19P
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 0.985.
(d)

To explain: Whether the probability increase as n (number of months) increased.
Answer to Problem 19P
Solution:
Yes, the standard deviation decreases as the sample size increases.
Explanation of Solution
The probability that
The probability is increased as sample size n increases, because as we increase the number of months (n), the standard deviation decreases and the probability increased.
(e)

To find: The
Answer to Problem 19P
Solution:
It is very unlikely if
Explanation of Solution
The sampling distribution for
Sample size,
We convert the interval
This means that the probability of the mean monthly return being below 1% after 2 years is 0.05%. This should be enough to shake your confidence in the statement that
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Chapter 7 Solutions
Understanding Basic Statistics
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