X is a binomial random variable.

n= 100 p= .4

Use the binomial approach and normal approximation to calculate the follwowing: 1. P(x>=38) 2. P(x=45) 3. P(X>45) 4. P(x <45)

Please Answer all the questions

Thank you

1. Suppose Bill can buy two goods, xylophones (X) and yogurt (Y). The utility he gains from these goods is shown in the table below.

1. If the price of xylophones is $2 per unit and the price of yogurt is $3 per unit, how many xylophones and yogurts will this consumer purchase, given an income of $17?
2. If the price of Y rises to $4.50 per unit, how much of X and Y will this consumer purchase, given an income of $17?

2. Suppose you decide to start your own business. You quit a job at which you earned $38,000 per year and invest $20,000 of your own money (which had been earning 10% in a mutual fund). You incur raw materials costs of $23,000. After 1 year you earn revenues of $23,000 at your new business. You decide to go back to your old job, and you sell your business for $20,000. A friend tells you "Hey, you broke even-- you got your money back when you sold the business." So, what do you think? What is the profit on your 1-year business venture? (Assume no other input costs, and be sure to count the sale of your business as income.)

Problem 2-32
Alimony (LO 2.3)

Jennifer divorced Ben in 2015. As part of negotiating the divorce settlement, Ben was to get the house worth $100,000 and alimony of $10,000 per year. Jennifer wanted to keep the house as it was close to her work and also had sentimental value so she offered to instead pay Ben alimony $60,000 in 2015, $60,000 in 2016, and $10,000 in 2017. Go to the IRS website (www.irs.gov) and print out Worksheet 1. Recapture of Alimonyfrom IRS Publication 504.

Complete the worksheet to determine how much income Jennifer must recapture in 2017.

A social researcher wants to test the hypothesis that college students may experience different levels of happiness depending on how much they are using social media. She surveyed students about the frequency of their social media use and their happiness. Among 10 heavy users, she found an average happiness score of 4.4 with a variance of 4.3, whereas the 10 light users reported an average happiness score of 6.5 with a variance of 3.4.

Answer the following questions:

1. What is the null hypothesis? (1 point)

2. What is the research hypothesis? (1 point)

3. What is the dependent variable? (1 point)

4. Write out the results of an independent samples t-test using these data. In other words, provide the numerical answers: t-statistic, your critical value of t (or p-value), and degrees of freedom. (4 points)

5. Write a paragraph to explain the results of the hypothesis test using statistics from the problem with alpha=0.05. This should be two or more formal sentences to describe your findings and conclusions. (3 points)

A social researcher wants to test the hypothesis that college students may experience different levels of happiness depending on how much they are using social media. She surveyed students about the frequency of their social media use and their happiness. Among 10 heavy users, she found an average happiness score of 4.4 with a variance of 4.3, whereas the 10 light users reported an average happiness score of 6.5 with a variance of 3.4.

Answer the following questions:

1. What is the null hypothesis? (1 point)

2. What is the research hypothesis? (1 point)

3. What is the dependent variable? (1 point)

4. Write out the results of an independent samples t-test using these data. In other words, provide the numerical answers: t-statistic, your critical value of t (or p-value), and degrees of freedom. (4 points)

5. Write a paragraph to explain the results of the hypothesis test using statistics from the problem with alpha=0.05. This should be two or more formal sentences to describe your findings and conclusions. (3 points)

a. Construct a regression model using all three independent variables. Let y be the final exam scores,x1 be the GPAs, x2 be the number of hours spent studying, and x3be the number of absences during the semester.

b.Calculate the multiple coefficient of determination

c.Test the significance of the overall regression model using significance=0.10

d.Calculate the adjusted multiple coefficent of determination

Score   GPA   Hours   Absences
67   2.53   3.0   0
68   2.25   4.0   3
69   2.60   2.5   1
71   3.11   0.5   0
75   3.08   6.0   4
76   2.74   3.5   6
76   3.36   1.5   0
78   2.98   3.0   3
78   2.99   2.0   3
80   2.83   2.5   2
80   2.79   4.5   0
83   3.46   7.0   1
82   3.24   3.0   1
83   3.14   3.0   4
83   3.19   5.5   0
85   2.96   2.0   0
83   2.71   4.0   1
84   3.19   4.5   3
84   3.73   2.0   0
85   3.56   3.5   2
85   2.91   6.0   1
85   3.06   6.5   1
86   3.16   5.0   3
88   3.90   7.5   4
87   3.54   4.0   0
90   3.34   6.5   1
88   3.66   5.0   0
89   2.88   3.5   1
91   3.41   6.0   1
92   3.20   4.5   2
91   3.80   7.0   0
91   3.92   6.0   2
92   3.99   5.0   0
91   3.59   6.5   1
93   2.97   4.0   2
93   3.27   6.5   0
97   2.88   3.5   0
100   3.74   5.0   1
101   3.48   6.5   1
101   3.00   7.0   0

a. Construct a regression model using all three independent variables. Let y be the final exam scores,x1 be the GPAs, x2 be the number of hours spent studying, and x3be the number of absences during the semester.

b.Calculate the multiple coefficient of determination

c.Test the significance of the overall regression model using significance=0.10

d.Calculate the adjusted multiple coefficent of determination

Score   GPA   Hours   Absences
67   2.53   3.0   0
68   2.25   4.0   3
69   2.60   2.5   1
71   3.11   0.5   0
75   3.08   6.0   4
76   2.74   3.5   6
76   3.36   1.5   0
78   2.98   3.0   3
78   2.99   2.0   3
80   2.83   2.5   2
80   2.79   4.5   0
83   3.46   7.0   1
82   3.24   3.0   1
83   3.14   3.0   4
83   3.19   5.5   0
85   2.96   2.0   0
83   2.71   4.0   1
84   3.19   4.5   3
84   3.73   2.0   0
85   3.56   3.5   2
85   2.91   6.0   1
85   3.06   6.5   1
86   3.16   5.0   3
88   3.90   7.5   4
87   3.54   4.0   0
90   3.34   6.5   1
88   3.66   5.0   0
89   2.88   3.5   1
91   3.41   6.0   1
92   3.20   4.5   2
91   3.80   7.0   0
91   3.92   6.0   2
92   3.99   5.0   0
91   3.59   6.5   1
93   2.97   4.0   2
93   3.27   6.5   0
97   2.88   3.5   0
100   3.74   5.0   1
101   3.48   6.5   1
101   3.00   7.0   0

Let a, b, c the last three digits of your QUID. Find the dimension of the rectangular box of maximum volume that can be inscribed in the ellipsoid (x/a)^2+(y/b)^2+(z/c)^2=1 a=4, b=8, c=9

Consider the following data for two variables,  and .

a. Develop an estimated regression equation for the data of the form . Comment on the adequacy of this equation for predicting . Enter negative value as negative number.

b. Develop an estimated regression equation for the data of the form . Comment on the adequacy of this equation for predicting . Enter negative value as negative number.

At the  level of significance, the relationship - Select your answer -isis notItem 34 significant; note that   of the variability in  has been explained by .

c. Predict the value of y when x=9.

(to 2 decimals)