1. Chloe plans to invest some of her savings into two blue-chip stocks, namely Stock A and Stock B. Suppose that the mean and standard deviation of the annual return of Stock A are 5% and 5%, respectively, and the mean and standard deviation for the annual return of Stock B are 10% and 10%, respectively. In this investment portfolio, Chloe will put 50% of her money into Stock A and 50% of her money into Stock B.

   1. (i) [3 marks] If the correlation coefficient of the two stock returns is -0.2, do you think that this investment portfolio can achieve diversification? (for this one, i think corr is the indicator of diversification, in this question, Corr=-0.2<0, which means achieve diversification. But the answer gives: "V[R]=26.25, cannot achieve portfolio diversification". please help, thx!

   2. (ii) [1 bonus mark] In order to achieve portfolio diversification, what advice will you give Chloe?

The heights of adult men in America are normally distributed, with a mean of 69.5 inches and a standard deviation of 2.65 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.7 inches and a standard deviation of 2.53 inches.

a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?

z =  

b) What percentage of men are shorter than 6 feet 3 inches? Round to the nearest tenth of a percent.



c) If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?

z =  

d) What percentage of women are TALLER than 5 feet 11 inches? Round to nearest tenth of a percent

Suppose that a person plays a game in which he draws a ball from a box of 10 balls numbered 0 through 9. He then puts the ball back and continue to draw a ball (with replacement) until he draws another number which is equal or higher than the first draw. Let X denote the number drawn in the first draw and Y denote the number of subsequent draws needed.

(a) Find the conditional probability distribution of Y given X = x, for x = 0, 1, · · · , 9.
(b) Find the joint probability distribution of X and Y , P(X = x, Y = y).
(c) Find the probability distribution of Y , P(Y = y).
(d) Find E(Y ).

Prove the following equivalences without using truth tables, and specify at each step of your proof the equivalence law you are using.

(a) ¬ (p ∨ (¬ p ∧ q)) ≡ ¬ p ∧ ¬ q

(b) ( x → y) ∧ ( x → z) ≡ x → ( y ∧ z)

(c) (q → (p → r)) ≡ (p → (q → r))

(d) ( Q → P) ∧ ( ¬Q → P) ≡ P

3.17 You and I play a tennis match. It is deuce, which means if you win the
next two rallies, you win the game; if I win both rallies, I win the game; if
we each win one rally, it is deuce again. Suppose the outcome of a rally is
independent of other rallies, and you win a rally with probability p. Let W be
the event “you win the game,” G “the game ends after the next two rallies,”
and D “it becomes deuce again.”
a. Determine P(W | G).
b. Show that P(W) = p2 + 2p(1 − p)P(W | D) and use P(W) = P(W | D)
(why is this so?) to determine P(W).
c. Explain why the answers are the same.

In a random sample of 26 ​people, the mean commute time to work was 30.7 minutes and the standard deviation was 7.2 minutes. Assume the population is normally distributed and use a​ t-distribution to construct a 80​% confidence interval for the population mean mu. What is the margin of error of mu​? Interpret the results. The confidence interval for the population mean mu is(-,-) ​(Round to one decimal place)

The margin of error of mu is___. ​(Round to one decimal place)

Interpret the results

.A. If a large sample of people are taken approximately 80​% of them will have commute times between the bounds of the confidence interval.

B. It can be said that 80​% of people have a commute time between the bounds of the confidence interval.

C. With 80​% ​confidence, it can be said that the population mean commute time is between the bounds of the confidence interval

D. With 80​% ​confidence, it can be said that the commute time is between the bounds of the confidence interval.  

Suppose the heights of adult women follow a normal distribution with a mean of 65.5 inches and a standard deviation of 2.75 inches. Determine the following:

1.) What percent of adult women are taller than 6 feet (72 inches)?

2.) What percent of adult women are taller than 5 feet (60 inches)?

3.) What percent of adult women are between 60 and 72 inches tall?

4.) Because of the high cost of materials, the company has decided that they cannot make pants in all sizes. Determine the heights that correspond to

a.) The bottom 8% of the population

b.) The upper 6% of the population

According to the National Bureau of Economic Research, the lengths of business cycles from 1919 to 1995, measured from trough to trough (a trough is the low point) in months, were 61 38 46 50 74 73 98 58 65 44 127 62 74 38 110 57 Find the Standard Deviation, mean, median, mode, and midrange

7. A political group randomly samples 60 potential voters to gauge the proportion of voters who favor a certain legislative issue. Assume the true proportion of voters who favor the issue is 75%. Find the probability that the sample fraction who favor the legislation will be within 0.10 of the true fraction.

Daily demand for cat litter at the Cat Café in Jones is 1500 ounces with a standard deviation of
300 ounces. The average lead time is 5 days and the standard deviation of lead time is 2 days.
Use this information to answer questions 44 to 46.

Suppose the café wants to peg their service level at 99.5%. What is the level of safety
inventory they should carry?
A) between 7500 and 7510 ounces
B) between 3070 and 3080 ounces
C) between 1950 and 1960 ounces
D) between 7910 and 7920 ounces

Suppose the café wishes to hold 7162 ounces of safety inventory. This is equal to how many
days of inventory?
A) 4.77 days
B) 5.12 days
C) 5.33 days
D) 5.67 days

Suppose the café wishes to carry 10,728 ounces as their safety inventory. What service level
would they achieve if standard deviation of demand over lead time is 3,074 ounces?
A) 93.9%
B) 99.98%
C) 95.2%
D) 95.7%

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 2.2 years, and standard deviation of 0.7 years.

If you randomly purchase 3 items, what is the probability that their mean life will be longer than 1 years? (Give answer to 4 decimal places.)

248
259
268
272
277
280
282
283
285
285
286
289
290
292
294
295
295
298
310
501

Because the mean is very sensitive to extreme​ values, it is not a resistant measure of center. By deleting some low values and high​ values, the trimmed mean is more resistant. To find the​ 10% trimmed mean for a data​ set, first arrange the data in​ order, then delete the bottom​ 10% of the values and delete the top​ 10% of the​ values, then calculate the mean of the remaining values. Use the axial loads​ (pounds) of aluminum cans listed below for cans that are 0.0111 in. thick. Identify any​ outliers, then compare the​ median, mean,​ 10% trimmed​ mean, and​ 20% trimmed mean.

Question 8 A factory uses a diagnosis test whether a part is defective or not. This test has a 0.90
probability of giving a correct result when applied to a defective part and a 0.05 probability
of giving an incorrect result when applied to a non-defective part. It is believed that one
out of every thousand parts will be defective.

(a) Calculate the posterior probability that a part is defective if the test says it is defec-
tive.
(b) Calculate the posterior probability that a part is non-defective if the test says it is
non-defective.
(c) Calculate the posterior probability that a part is misdiagnosed.

Ms. Smith teaches three Algebra I classes that cover exactly the same content. She is wondering if changing the order of some of the lessons would be beneficial to students. In class A, she teaches everything in the traditional order. In class B, she decides to skip Chapter 1 as it is preliminary information that students may already know. In class C, she decides to do Chapter 5 prior to doing Chapter 3. She would like to know if there are any significant differences in the average scores of the three classes.

1. Which test will be used?
2. What are H0 (null hypothesis) and Ha (alternative hypothesis)?
3. Calculate thes tatistic.
4. What decision does this inform to make and why? (may use the critical value in the chart or the calculated p-value, but must indicate what are doing.)
5. a one to two sentence conclusion that correctly responds to the question. 2 or 3 sentences to report your statistic ex. [χ^2(df)=1.1, p<.05]

he table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, y^=b0+b1x , for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant.

Price in Dollars 25 33 34 45 48

Number of Bids 2 3 4 5 7

1 of 6: Find the estimated slope. Round your answer to three decimal places.

2 of 6: Find the estimated y-intercept. Round your answer to three decimal places.

3 of 6: Find the estimated value of y when x=34x=34. Round your answer to three decimal places.

4 of 6: Determine if the statement "Not all points predicted by the linear model fall on the same line" is true or false.

5 of 6: According to the estimated linear model, if the value of the independent variable is increased by one unit, then the change in the dependent variable yˆy^ is given by?

6 of 6: Find the value of the coefficient of determination. Round your answer to three decimal places.