Sections 6.1,6.2,1. (6 pts) Real Estate Investment. Jack and Jill purchase a for

Question

Sections 6.1,6.2,1. (6 pts) Real Estate Investment. Jack and Jill purchase a foreclosed property for Assignment $50,000 and spend an additional $27,000 fixing up the property. They feel that they can resell the property for $120,000 with probability 0.15, $100,000 with probability 0.45, $80,000 with probability 0.25, and $60,000 with probability 0.15. Compute and interpret the expected profit for reselling the property 2. (12 pts) Suppose that the talk time on the Apple iPhone is approximately normally distributed with mean 7 hours and standard deviation 0.8 hours. For each problem below, sketch the normal curve and shade the area to be found by hand. Use the corresponding z-values and Table V (not technology). 8.1,8.2 a) b) c) d) e) f) What proportion of the time will a fully charged iPhone last at least 6 hours? What is the probability a fully charged iPhone will last less than 4 hours? what talk time represents the cutoff for the top 3% of all talk times? Determine the talk time that is at the 15th percentile. Would it be unusual for an iPhone to last more than 8.5 hours? Explain. Find the talk tines that represent the middle 90% of iPhone talk times. 3. (10 pts) In 2013, the average length of a feature length film was 86 minutes with a standard deviation of 24 minutes. Source: IMDB.com/interfaces a) b) c) d) Will the proportion found in c) be greater than or less than the proportion Explain why it is inappropriate to use the normal model to find the probability that a random sample of 15 films will have a mean length greater than 115 minutes. Describe the sampling distribution of X for n-40 films (Shape, Center, Spread, with justification) Find the proportion of samples of size n- 40 that will have a mean length greater than 115 minutes. of samples of size n- 65 that will have a mean length greater than 115 min? Explain. There is a 4% probability that a random sample of 40 films will have a mean length greater than e) For #4, round proportions to 3 d.p. and standard deviations to 4 d.?. 4. (5 pts) The Bechdel test is a study of gender bias in feature films. The test determines if feature films meet three requirements: i) has at least two named women in it, ii) who talk to each other, iii about something other than a man. In 2013, 1,698 of the 3,703 films directed by a man passed the Bechdel test. a) Describe the sampling distribution of p - the proportion of films directed by a man that will pass the Bechdel test in a random sample of 50 films. (Shape, Center, Spread, with justification.) b) Find and interpret P(04

Explanation / Answer

Solution Q1 [All figures are in 105.]

Purchase Price = 0.5

Property Fixing Cost = 0.27

Total Cost, C = 0.77

If the selling price is S, then Profit, P = S – 0.77 ……………………………….........................................……….(1)

Back-up Theory

If a discrete random variable, X, has pmf (probability mass function) p(x), x = x1, x2, …., xn, then, expected value, of X = E(X) = sum{x.p(x)} summed over all possible values of x….................................................................... (2)

Expected value of a function f(x) of variable X = E{f(X)} = sum{f(x).p(x)} summed over all possible values of x…..…(3)

Now, to work out the answer,

Here, S is the random variable and P = S – 0.77 is f(S). Thus, vide (3), expected profit,

E(P) = ?[i = 1, 4]{(Si – 0.77)P(Si)} = 0.15 x 105

= $15000 ANSWER

Details of Calculations

i

1

2

3

4

Total

Si

1.2

1

0.8

0.6

(Si - 0.77)

0.43

0.23

0.03

-0.17

P(Si)

0.15

0.45

0.25

0.15

1

(Si - 0.77)xP(Si)

0.0645

0.1035

0.0075

-0.0255

0.15

DONE

i

1

2

3

4

Total

Si

1.2

1

0.8

0.6

(Si - 0.77)

0.43

0.23

0.03

-0.17

P(Si)

0.15

0.45

0.25

0.15

1

(Si - 0.77)xP(Si)

0.0645

0.1035

0.0075

-0.0255

0.15

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