1 answer

Yearly Returns for stocks is normally distributed  around a mean of 9% with a standard deviation of...

Question:

Yearly Returns for stocks is normally distributed  around a mean of 9% with a standard deviation of 12%. A random sample of 2000 stock returns is shown on the Stock Returns worksheet.

(6) (To three decimal places) what is the probability of a stock having a negative yearly return?

(7)(Tothree decimal places) what is the probability of a stock having a yearly return between 5% and 8%?

(8) (To three decimal places) What is the relative frequency of stocks, from the random sample on the Stock Returns worksheet, that had a negative yearly return?

(9) (To three decimal places) What is the relative frequency of stocks, from the random sample on the Stock Returns worksheet, that had between 5% and 8% for a yearly return?

(10) (To three decimal places) what yearly return is exceeded 80% of the time?

Can you tell me which excel function to use for each question and how to solve it?


Answers

Solution Q6 and Q7

Let X = Yearly Returns (in %) for stocks. Then, we are given X ~ N(9, 122) ………………… (1)

Back-up Theory

If a random variable X ~ N(µ, σ2), i.e., X has Normal Distribution with mean µ and variance σ2, then, Z = (X - µ)/σ ~ N(0, 1), i.e., Standard Normal Distribution and hence

P(X ≤ or ≥ t) = P[{(X - µ)/σ} ≤ or ≥ {(t - µ)/σ}] = P[Z ≤ or ≥ {(t - µ)/σ}] .………........………...…(2)

Probability values for the Standard Normal Variable, Z, can be directly read off from Standard Normal Tables ………… (3a)

or can be found using Excel Function: Statistical, NORMSDIST(z) which gives P(Z ≤ z) …..............................................(3b)

Now to work out the solution,

Q6

Probability of a stock having a negative yearly return

= P(X < 0)

= P[Z < {(0 - 9)/12}] [vide (2) and (1)]

= P(Z < - 0.75)

= 0.2266 [vide (3b)] Answer

Q7

Probability of a stock having a yearly return between 5% and 8%

= P(5 < X < 8)

= P[{(5 - 9)/12} < Z < {(8 - 9)/12}] [vide (2) and (1)]

= P(- 0.3333 < Z < - 0.0833)

= P(Z < - 0.0833) - P(Z < - 0.3333)

= 0.4668 – 0.3695 [vide (3b)]

= 0.0973 [vide (3b)] Answer

Now to respond to the specific query, ‘which excel function to use’,

The appropriate Excel function is: Statistical, NORMSDIST.

A concise write up on how to use this function is given below:

Method to find probability using Excel Function for Standard Normal Distribution

In Excel Worksheet, click ‘fX’. Screen displays ‘Insert Function’ In the window ‘Search for a function’ type ‘NORMSDIST’ and click ‘Go’. Under ‘Select a function’, NORMSDIST appears. Click ‘Ok’

Screen displays just one window, z.

Against ‘z’ window, type the z value for which probability is required. Required probability, is displayed below the window against ‘=’ sign.

Note that the above probability value is the cumulative probability of less than or equal to the z-value typed in the window.

Examples

To find P(Z ≤ - 0.0833), type -0.0883 in z-window and display would be 0.4668.

Similarly, to find P(Z ≤ - 0.3333), type -0.3333 in z-window and display would be 0.3695.

DONE

Unable to give solutions for Q8 to Q10 since Stock Returns worksheet data is not given along with the question.

.

Similar Solved Questions

1 answer
Sora Industries currently has 60 million outstanding shares, $120 million in debt and $40 million in...
Sora Industries currently has 60 million outstanding shares, $120 million in debt and $40 million in cash. Sales in the last financial year were $433. They are projected to grow at 8.1% next year, 10.3% in the second year, and 6% in the third year. From the fourth year onwards, sales will grow at 5%...
1 answer
1.5 pts Question 9 Fat metabolism occurs when glucose is not available for energy. When would...
1.5 pts Question 9 Fat metabolism occurs when glucose is not available for energy. When would fat metabolism occur? When a person has not eaten for several minutes When a person has not eaten for several hours When a person is consuming a low-carbohydrate diet When a person is in ketosis When a pers...
1 answer
Please cash flow diagram. West Coast Marine and RV is considering replacing its wired pendant controllers...
Please cash flow diagram. West Coast Marine and RV is considering replacing its wired pendant controllers on its heavy-duty cranes with new portable infrared keypad controllers. The company expects to achieve cost savings of $38,000 the first year and amounts increasing by $1,500 each year thereafte...
1 answer
Please solve, show work, and give detail explanation 11. The IRR decision rule is unreliable when...
Please solve, show work, and give detail explanation 11. The IRR decision rule is unreliable when comparing mutually exclusive projects. a. True b. False 12. Return on Assets (ROA) is an example of a profitability ratio. a. True b. False 13. For a given time period, the higher the interest rate, the...
1 answer
If a 24.51 g sample of an unknown compound decomposes to produce 14.91 g KCl and...
If a 24.51 g sample of an unknown compound decomposes to produce 14.91 g KCl and 9.60 g O2, what is its empirical formula? [5 marks]...
1 answer
Layout References A A Aay to x Avo Av Mailings Review View Tell me what you...
Layout References A A Aay to x Avo Av Mailings Review View Tell me what you want to do Eva A EE EE av AalbCcDdee Predict the major product of the following reaction. Br2, FeBrz English (United States)...
1 answer
3. Let n be an integer. Prove that 2 (n4 – 3) if and only if...
3. Let n be an integer. Prove that 2 (n4 – 3) if and only if 4| (n2+3)....
1 answer
What is the main component of PAYG? 30–50 words
What is the main component of PAYG? 30–50 words...
1 answer
A car is initially at rest on a straight road. The graph shows the acceleration of...
A car is initially at rest on a straight road. The graph shows the acceleration of the car along that road as a function of time. What distance does the car cover in the first 9 seconds? 4. 2 -1 -3 0 1 2 34 5 6 7 8 9 10 11 12 13 14 t (s)...
1 answer
6. (5 pts) To find molecular weight of an unknown compound, 0.112 g of the unknown...
6. (5 pts) To find molecular weight of an unknown compound, 0.112 g of the unknown is dissolved in 40.0 g of water. The resulting solution freezes at -0.049 °C. Find molar mass of the unknown....
1 answer
Suppose the F and G genes are on the same chromosome and separated by 75 map...
Suppose the F and G genes are on the same chromosome and separated by 75 map units What fraction of the progeny from the cross FG/fg times fg/fg are expected to be Fg/fg? 12.5% 50% 25% 37.5% Two genes cannot be separated by 75 map units....
1 answer
NMRR The 'H NMR for the unknown 0.0 7.5 7.0 6.5 6.0 5 5 .0 4.5...
NMRR The 'H NMR for the unknown 0.0 7.5 7.0 6.5 6.0 5 5 .0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 ppm Proton peak Integration Chemical Shift Neighbors (A) Splitting pattern (+1) (report as singlet/doublet/tripletlete. (היי C must be an aliphatic alcohol. There is a strong O-H stre...
1 answer
Two corners of a triangle have angles of # (5 pi )/ 12 # and # pi / 6 #. If one side of the triangle has a length of 5, what is the longest possible perimeter of the triangle?
Two corners of a triangle have angles of # (5 pi )/ 12 # and # pi / 6 #. If one side of the triangle has a length of 5, what is the longest possible perimeter of the triangle?...
1 answer
424. You are the nurse caring for 82 year old women in the PACU. The woman...
424. You are the nurse caring for 82 year old women in the PACU. The woman begins to awaken and responds to her name but is confused, restless and agitated. What are you aware of? A. Postoperative confusion is an indication of an oxygen problem or possibly a stroke during surgery. B. Confusion, rest...