Blue Chip Stocks. “Blue chip” is a term used to describe large, long-standing co

Question

Blue Chip Stocks. “Blue chip” is a term used to describe large, long-standing companies with a stable reputation. They are generally considered to be safe, fiscally conservative investment opportunities. Suppose that during any given month, the return on stocks invested in blue chip companies follow a non-normal distribution with mean µ = 1.24% and a standard deviation of = 2.1%.

(a) (Free Response) Given the tools we have learned in class, can you find the probability that a randomly selected blue chip company has a return of more than 1.4% next month? Explain why or why not. 1

(b) Suppose you randomly selected 9 blue chip companies and recorded their returns at the end of the month. Remember that we can think of the observed sample mean, ¯x, as a single draw from a distribution that relates to the random variable X¯. We call this distribution the sampling distribution of the sample mean.

i. What is the mean of the sampling distribution of the sample mean when n = 9?

ii. What is the standard error of the sampling distribution of the sample mean when n = 9?

iii. What is the shape of the sampling distribution of the sample mean when n = 9? • Normal • Approximately Normal • Not Normal

iv. Given the tools we have learned in class, can you find the probability that the mean return of the 9 stocks is less than 1.0%? (Choose one) Yes or No

(c) Now suppose you have a random sample of n = 49 blue chip companies and their corresponding returns after a period of 1 month.

i. What is the mean of the sampling distribution of the sample mean when n = 49?

ii. What is the standard error of the sampling distribution of the sample mean when n = 49?

iii. What is the shape of the sampling distribution of the sample mean when n = 49? • Normal • Approximately Normal • Not Normal

(d) Find the probability that the mean return for the 49 randomly sampled blue chip companies is less than 1.0%.

i. Report the z-score corresponding to 1.0%.

ii. Report the final probability to 4 decimal places using Table A (z-table).

(e) Find the probability that the mean return for the 49 randomly sampled blue chip companies is between 1.0% and 1.84%.

i. Report the z-scores corresponding to 1.0% and 1.84%.

ii. Report the final probability to 4 decimal places using Table A.

(f) What is the value that corresponds the 85th percentile of the sampling distribution of the sample mean of the returns for the 49 blue chip companies? Compute this value and round the answer to two decimal places.

Explanation / Answer

Part a

Assuming long term normality of the data for large sample size, we have to find the P(X>1.4)

We are given mean = 1.24 and SD = 2.1

P(X>1.4) = 1 – P(X<1.4)

Z = (X – mean) / SD

Z = (1.40 – 1.24) / 2.10

Z = 0.076190476

P(X<1.4) = P(Z< 0.076190476) = 0.53036622

P(X>1.4) = 1 – P(X<1.4)

P(X>1.4) = 1 – 0.53036622

P(X>1.4) = 0.46963378

Required probability = 0.46963378

Part b.i.

We know the estimate for the mean of the sampling distribution of the sample mean is given as the population mean µ.

Estimate of mean of sampling distribution of sample mean = µ = 1.24%

Part b.ii.

The formula for the standard error of the sampling distribution of the sample mean is given as below:

Standard error = /sqrt(n)

We are given = 2.1 and n = 9

Standard error = 2.1/sqrt(9) = 2.1/3 = 0.7

Standard error = 0.70

Part b.iii.

What is the shape of the sampling distribution of the sample mean when n = 9?

The shape of the sampling distribution of the sample mean is approximately normal.

Answer: Approximately Normal

Part b.iv.

Given the tools we have learned in class, can you find the probability that the mean return of the 9 stocks is less than 1.0%?

Answer: Yes

.....Because, we can use the sampling distribution of the sample mean which follow approximately normal distribution.

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