I had some questions on the following problems:
1. You solicit 100 pledges for a charitable organization. Each pledge is likely to be $10, $50, or $100. You may use the fact that the standard deviation of the three amounts $10, $50 and $100 is $37.
What are the chances that the 100 pledges total more than $5,700?
- How will the standard deviation help me here?
2. There are two candidates running for governor in CA and they are said to have roughly equal support from the voters. To get a better idea who is ahead, a company polls 400 of the 20 million registered voters in California. Likewise, there are two candidates running for mayor in Palo Alto who are said to have roughly equal support, and the company polls 400 out of the 20,000 registered voters in Palo Alto. Will the first poll be more accurate, equally accurate or less accurate than the second poll?
- How does population size impact sample accuracy?
3. The average taxable income reported on tax returns for the year 2016 is $45,000, and the standard deviation of the taxable incomes is $23,000. Which of the following statements are true? Both?
...The percentage of taxable incomes that fall below $30,000 can be computed from that above information using normal approximation.
... The chances that the sum of 100 randomly selected taxable incomes exceeds $4 million can be computed from the above information using normal approximation.
- When can you apply normal approximation?
1. You solicit 100 pledges for a charitable organization. Each pledge is likely to be $10, $50, or $100. You may use the fact that the standard deviation of the three amounts $10, $50 and $100 is $37.
What are the chances that the 100 pledges total more than $5,700?
- How will the standard deviation help me here?
2. There are two candidates running for governor in CA and they are said to have roughly equal support from the voters. To get a better idea who is ahead, a company polls 400 of the 20 million registered voters in California. Likewise, there are two candidates running for mayor in Palo Alto who are said to have roughly equal support, and the company polls 400 out of the 20,000 registered voters in Palo Alto. Will the first poll be more accurate, equally accurate or less accurate than the second poll?
- How does population size impact sample accuracy?
3. The average taxable income reported on tax returns for the year 2016 is $45,000, and the standard deviation of the taxable incomes is $23,000. Which of the following statements are true? Both?
...The percentage of taxable incomes that fall below $30,000 can be computed from that above information using normal approximation.
... The chances that the sum of 100 randomly selected taxable incomes exceeds $4 million can be computed from the above information using normal approximation.
- When can you apply normal approximation?
