Statistics Homework

1. Let Z be a standard normal random variable. Calculate the following probability Use Round your response to at least three decimal places

a. P (Z ≤ -1.61) =

b. P (Z > 0.83) =

c. P ( -0.78 < Z < 2.19) =

2. Let Z be a standard normal random variable. Calculate the following probabilities Round your response to at least three decimal places

a. P (Z ≤ -1.94) =

b. P (Z > 1.32) =

c. P (-1.09 < Z < 2.20) =

3. Let Z be a standard normal random variable, to determine the value of c

For Z – values less than -3.70, use Area = 0.0001

For Z -values greater than 3.69, use Area = 0.9999

P (-c ≤ Z ≤ c) – 0.9500

4. Let Z be a standard normal random variable, use the calculator provided to determine the value of c.

P (Z ≤ c) = 0.1446

Carry your intermediate computations to at least four decimals places. Round your answer to two decimal places.

5. Let Z be a standard normal random variable. Use the calculator provided to determine the value of c.

P (c ≤ Z ≤ -0.77) = 0.1938

Carry your intermediate computations to at least four decimals places. Round your answer to two decimals places

6. Let Z be a standard normal random variable. use the below formula to determine the value of c

P (-0.62 ≤ Z ≤ c) = 0.7177

Carry your intermediate computations to at least four decimals places. Round your answer to two decimal places.

7. Risk taking is an important part of investing. In order to make suitable investment decisions on behalf of their customers, portfolio managers give a questionnaire to new customers to measure their desire to take financial risks. The scores on the questionnaire are approximately normally distributed with a mean of 50 and a standard deviation of 14. The customers with scores in the bottom 15% are described as risk averse. What is the questionnaire score that separates customers who are considered risk averse from those who are not? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place

8. Suppose that scores on a particular test are normally disturbed with a mean of 120 and a standard deviation of 20. What is the minimum score needed to be in the top 15% of the scores on the test? Carry your intermediate computations to at least four decimal places, and round your answer to one decimal place

9. Suppose that the speeds of cars traveling on California freeways are normally distributed with a mean of 60 miles/hour. The highway patrol’s policy is to issue tickets for cars with speeds exceeding 75 miles/hour. The record show that exactly 1% of the speeds exceed this limit. Find the standard deviation of the speeds of cars traveling on California freeways. Carry your intermediate computations to at least four decimal places, and round your answer to one decimal place

10. Suppose that IQ scores in one region are normally distributed with a standard deviation of 18. Suppose also that exactly 52% of the individuals from this region have IQ scores of greater than 100 (and that 48% do not). What is the mean IQ score for this region? Carry your intermediate computations to at least four decimal places, and round your answer to one decimal place

11. Suppose that the time required to complete a 1040R tax form is normally distributed with a mean of 110 minutes and a standard deviation of 20 minutes. What proportion of 1040R tax form will be completed in at most 73 minutes? Round you answer to at least four decimal places.

12. For a standardized psychology examination intended for psychology majors, the historical data show that scores have a mean of 515 and a standard deviation of 175. The grading process of this year’s exam has just begun. The average score of the 40 exams graded so far is 512. What is the probability that a sample of 40 exams will have a mean score of 512 or more if the exam scores follow the same distribution as in the past? Carry your intermediate computations to at least four decimal places, and round your answer to at least three decimal places

13. Suppose that the heights of adult men in the United States are normally distributed with a mean of 70 inches and a standard deviation of 3.5 inches. What proportion of the adult men in the United states are less than 6 feet tall? Hint 6 feet = 72 inches. Round your answer to at least four decimals

14. Seventy million pounds of trout are grown in the U.S. every year. Farm raised trout contain an average of 32 grams of fat per pound, with a standard deviation of 7.5 grams of fat per pound. A random sample of 34 farm -raised trout is selected. The mean fat content for the sample is 31.1 grams per pound. Find the probability of observing a sample mean of 31.1 grams of fat per pound or less in a random sample of 34 farm-raised trout? Carry your intermediate computations to at least four decimal places, and round your answer to at least three decimal places.

15. Suppose that a new treatment is successful in curing a common ailment 71% of the time. If the treatment is tried on a random sample of 145 patients approximate the probability that at most 103 will be cured. Use the normal approximation to the binomial with a correction for continuity. Round you answer to at least three decimal places. Do not round any intermediate steps.

16. A manufacturing process produces semiconductor chips with a known failure rate of 5.5%. If a random sample of 235 chips is selected, approximate the probability that more than 9 will be defective. Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimals places. Do not round any intermediate steps.