# MATHEMATICS

Don’t need to show work. TI-83/T-84 Recommended to use.

1) Last year a survey of people in the State of Kansas reported that 30% of people reported that they had been a tornado at some time in their lives. How many people must be surveyed this year to estimate the percentage of people in the State of Kansas who have been in a tornado at some time in their lives if we want to be 94% confident that our estimate is within 4% of the true population percentage? Round up to the next whole number.

2)In a local school district it was found that in a random sample of 1550 students, 785 of those students brought their own lunch to school. What is the Margin of Error for the 99% confidence interval estimate for the true percentage of students who bring their lunchto school. Answer as a percent rounded to the nearest tenth.

3)Find the t(α/2) for a 80% confidence interval based on a sample size of 12.
Use the t – distribution table to find this value to the thousandth decimal place.

4)To qualify for the Police Academy, candidates must score in the top 7% on the General Abilities Test. The mean and standard deviation of the General Abilities Test are 350 and 15 respectively. What is the lowest score that a candidate can have and still qualify for the Police Academy? Your answer should be “rounded up” to the nearest whole number.

5)Find the 2 z – scores in the standard normal distribution that define the middle 70% of the area under the curve. (Round your answer to the nearest hundredth decimal place). Give you answers in ascending order separated by a comma.

6)In a “standard normal distribution”, find the area under the curve for z – scores above – .5; (Round your answer to 4 decimal places)

7)Lengths of pregnancies are normally distributed with a mean of 265 days and a standard deviation of 15 days.
What is the z – score for a pregnancy lasting 275 days? (Round to the nearest hundredth)

8)Find the z – score in the standard normal distribution such that 25% of the area under the curve will be to the right of this z – score. (Round your answer to the nearest hundredth decimal place).

9)The average beginning annual salary for teachers in California is \$41,181. Assume that this is a normal distribution with a standard deviation of \$725. 10% of starting teachers in California will make “at most” (not more than) how much money per year?(Round to the nearest dollar)

DO NOT Include a \$ sign OR a comma in your answer.

10)The amount of money that a student at Harvard University carries on his/her person is normally distributed with a mean of \$50 and a standard deviation of \$10. What is the probability that a randomly selected Harvard University student will have more than \$75 on his/her person?

11)Woman’s heights are normally distributed with a mean of 64.5 inches and a standard deviation of 2.3 inches. If a woman is selected at random, what will be the probability that her height will be between 64 and 65 inches? (Give your answer as a decimal rounded to 4 places).

12)The average number of hours that a student at San Jose State University (SJSU) spends per day working at a computer is 4.3 hours. This distribution is normally distributes with a standard deviation of 0.8 hours. What percentage of SJSU students spend less than 5.5 hours per day working at a computer? Give you answer as a decimal rounded to four decimal places.

13)The DMV reports that the average age of a vehicle in Santa Clara County is 9 years old (108 months). Assume that the distribution of vehicle ages is normally distributed with a standard deviation of 18 months. What percent of vehicles in Santa Clara County are less than 8 years old (96 months). Give you answer as a decimal rounded to four decimal places.

14)AAA reports that the average time it takes to respond to a roadside emergency is 25 minutes.with a standard deviation of 4.5 minutes. For a randomly selected sample of 10 emergency response calls what is the probability that the average wait time is more than 28 minutes for a roadside emergency? (Give you answer as a rounded 4 place decimal).

15a)The average number of hours that a student at San Jose State University (SJSU) spends per day working at a computer is 4.3 hours. This distribution is normally distributes with a standard deviation of 0.8 hours. What percentage of SJSU students spend less than 5.5 hours per day working at a computer? (Express your answer as a decimal rounded to four decimal places.)

15b)The average number of hours that a student at San Jose State University (SJSU) spends per day working at a computer is 4.3 hours with a standard deviation of 0.8 hours. What is the probability that a randomly selected sample of 16 SJSU students will spend an average of less than 4.5 hours per day working on a computer?

16)AAA reports that the average time it takes to respond to a roadside emergency is 25 minutes.with a standard deviation of 4.5 minutes. For a randomly selected sample of 12 emergency response calls what is the probability that the average wait time is between 24 and 27 minutes for a roadside emergency? (Give you answer as a rounded 4 place decimal).

17)Woman’s heights have a mean of 64.5 inches and a standard deviation of 2.3 inches. What will be the probability that a randomly selected sample of 30 women will have an average height greater than 65 inches? (Give your answer as a decimal rounded to 4 places).

18)A California State Lottery official wishes to estimate the average amount of money that a person in the State of California who plays the lottery spends on Lottery tickets in a given month. He wants to be 90% confident in his estimate. He randomly samples 150 people who play the California State Lottery and finds that for this sample the average amount spent is \$ 39.50 with a sample standard deviation of \$3.50. What is the lower boundary of the confidence interval estimate to the nearest penny? Please use a dollar sign in expressing your answer to the nearest cent.

19)In a recent survey of men in the State of California, 590 men of 1,500 randomly sampled said that they supported the death penalty. What is the best point estimate of the true population percentage of men in the State of California supporting the death penalty based on this survey? Answer as a percent rounded to the nearest tenth of a percent.

20)A statistics student would like to estimate the average age of students at her college. She would like to be 99% confident that her estimate includes the actual college population mean. She did a smaller preliminary survey and found that a reasonable estimate of the population standard deviation was 3 1/2 years. How many people must she survey if she wants to be within 1/4 year of the true population mean?(Do not use any commas in your answer)

21)In a local school district it was found that in a random sample of 1550 students, 785 of those students brought their own lunch to school. What is the Margin of Error for the 99% confidence interval estimate for the true percentage of students who bring their lunch to school. Answer as a percent rounded to the nearest tenth.

22)A political pollster wishes to estimate the percentage of female voters who believe in a “Woman’s Right to Choose”. He wants to be 90% confident that his estimate is within 10% of the true population percentage of female voters who believe in a “Woman’s Right to Choose”. What is the minimum number of female voters that this political pollster need to sample randomly in order to accomplish this task? Round your answer “up” to the nearest counting number. Do not use any commas in your answer.

23)A researcher is conducting a study about the average amount of tire tread wear for cars on the road today. The tread depth of the left front tire is measured in 18 randomly selected cars on the road today. The sample mean was found to be .33 inches and the sample standard deviation was found to be .07 inches. Find the 99% confidence interval estimate for the average amount of tire tread wear based on this sample. Assume that the variable is normally distributed.

Give your answer as the interval defining values in ascending order separated by a comma.
For example .53,.51 DO NOT USE PARENTHESES Round the answers to the hundredth decimal place.

24)The math scores for a sample of 100 eighth graders had a mean of 80 with a sample standard deviation of 9. What is the best point estimate for the estimate of the population mean of the math scores for all eighth graders?

25)A California State Lottery official wishes to estimate the average amount of money that a person in the State of California who plays the lottery spends on Lottery tickets in a given month. He wants to be 95% confident in his estimate. He randomly samples 150 people who play the California State Lottery and finds that for this sample the average amount spent is \$ 39.50 with a sample standard deviation of \$3.50. What is the upper boundary of the confidence interval estimate to the nearest penny? Please use a dollar sign in expressing your answer to the nearest cent.

26)Find the Z(α/2) for a 80% confidence interval.
Your answer should be a positive decimal rounded to the hundredths place.

27)Find the t(α/2) for a 80% confidence interval based on a sample size of 12.
Use the t – distribution table to find this value to the thousandth decimal place.

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