Question

Can anybody help me solve these?

1. Suppose the average number of hours worked per week for high-school aged teens in the US is 17 hours per week with a standard deviation of 4 hours. A high school teacher working at an inner city high school is concerned about the time students spend working at after school jobs. She randomly selects 15 of her students and records the number of hours they spend working each week. Supposing that her students conform to the national average, construct a box model for the average work hours of students in the sample. a.

The number of draws is ___________.

b. The average of the tickets in the box is ___________.

c. The SD of the tickets in the box is __________. 2.

In 2009, the average age of women in the US at the time of their first marriage was 26.9 years. Suppose the SD is 5 years and that a researcher is planning to take a random sample of 150 women. Construct a box model for the average age at first marriage in the sample.

a. The number of draws is ___________.

b. The average of the tickets in the box is ___________.

c. The SD of the tickets in the box is __________.

3. The spinner for a child’s board game has five equally-sized colored regions, one of which is green. If we spin the spinner 50 times, construct a box model for the percentage of times the spinner lands on green.

a. The number of draws is ___________.

b. The average of the tickets in the box is ___________.

c. The SD of the tickets in the box is __________.

4. According to a genetic theory, there is a 10% chance that a randomly selected person from a large population has a given gene. I plan to take a simple random sample of 500 people from this population. Construct a box model for the percentage of people in the sample with this gene.

a. The number of draws is ___________.

b. The average of the tickets in the box is ___________.

c. The SD of the tickets in the box is __________.

5. An insurance company states that 84% of its claims are settled within 30 days. A consumer group selects a random sample of 475 of the company’s claims. Construct a box model for the percentage of claims in the sample that are settled within 30 days.

a. The number of draws is ___________.

b. The average of the tickets in the box is ___________.

c. The SD of the tickets in the box is __________.

Answer 1

1. Suppose the average number of hours worked per week for high-school aged teens in the US is 17 hours per week with a standard deviation of 4 hours. A high school teacher working at an inner city high school is concerned about the time students spend working at after school jobs. She randomly selects 15 of her students and records the number of hours they spend working each week. Supposing that her students conform to the national average, construct a box model for the average work hours of students in the sample. a.

The number of draws is 15

b. The average of the tickets in the box is 17

c. The SD of the tickets in the box is 17/\sqrt{15}= 4.389

2.In 2009, the average age of women in the US at the time of their first marriage was 26.9 years. Suppose the SD is 5 years and that a researcher is planning to take a random sample of 150 women. Construct a box model for the average age at first marriage in the sample.

a. The number of draws is 150

b. The average of the tickets in the box is 26.9

c. The SD of the tickets in the box is 26.9//sqrt{150}=2.1963

3. The spinner for a child’s board game has five equally-sized colored regions, one of which is green. If we spin the spinner 50 times, construct a box model for the percentage of times the spinner lands on green.

a. The number of draws is 50

b. The average of the tickets in the box is 8.33

Expected value = 1/6*50 = 8.33

c. The SD of the tickets in the box is 6.94
Standard deviation = (1/6)*(5/6)*50 = 6.94

4. According to a genetic theory, there is a 10% chance that a randomly selected person from a large population has a given gene. I plan to take a simple random sample of 500 people from this population. Construct a box model for the percentage of people in the sample with this gene.

a. The number of draws is 500

b. The average of the tickets in the box is 50
expected value = 0.1*500 = 50

c. The SD of the tickets in the box is 45
standard deviation = (0.1)*(0.9)*(500) = 45

5. An insurance company states that 84% of its claims are settled within 30 days. A consumer group selects a random sample of 475 of the company’s claims. Construct a box model for the percentage of claims in the sample that are settled within 30 days.

a. The number of draws is 475

b. The average of the tickets in the box is 399
Expected value = 0.84*475 = 399

c. The SD of the tickets in the box is 0.016821
standard deviation = \sqrt{\frac{0.84(1-0.84)}{475}}= 0.016821