1. Suppose Z follows the standard normal distribution. Calculate the following probabilities using the ALEKS calculator round your responses to at least three decimal places.

(A) P(2 <= - 1.73) =

(B) P(Z > - 1.1) =

(C) P(1.03 < Z < 2.13) =

2. Suppose Z follows the standard normal distribution. Calculate the following probabilities using the ALEKS calculator Round your responses to at least three decimal places

(A) P(Z > - 0.5) =

(B) P(Z <= 2.03) =

(C) P(- 0.35 < Z < 1.67) =

3. Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of so that the following is true. P(-CZc)= 0.9297

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

4. Suppose Z follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of so that the following is true. P(-CZc)= 0.9127

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

5. Suppose Z follows the standard normal distribution Use the calculator provided, or this table to determine the value of c so that the following is true.

P(cZ - 1.24) = 0.0746

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

6. Suppose Z follows the standard normal distribution Use the calculator provided, or this table to determine the value of c so that the following is true.

P(1.17Z c) = 0.1060

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

9. 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 of50and a standard deviation of 16. The customers with scores in the bottom15 %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.

10. The distribution of scores on a standardized aptitude test is approximately normal with a mean of500and a standard deviation of105. What is the minimum score needed to be in the top20%on this test?

Carry your intermediate computations to at least four decimal places, and round your answer to the nearest integer

11. Suppose that the creatine kinase levels among healthy males are normally distributed with a standard deviation of22units/L. Research shows that exactly5% of the healthy males have a creatine kinase level above152units/L.What is the mean creatine kinase level in healthy males?

Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.

____ units/L

12. Suppose that IQ scores in one region are normally distributed with a standard deviation of16. Suppose also that exactly58%of the individuals from this region have IQ scores of greater than100(and that42%do not). What is the mean IQ score for this region?

Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.

13. Suppose that the annual rate of return for a common biotechnology stock is normally distributed with a mean of6.5% and a standard deviation of5%. Find the probability that the one-year return of this stock will be positive. Round your answer to at least four decimal places.

14. For a standardized psychology examination intended for psychology majors, the historical data show that scores have a mean of520 and a standard deviation of170. The grading process of this year's exam has just begun. The mean score of the35 exams graded so far is518. What is the probability that a sample of35exams will have a mean score of518 or more if the exam scores follow the same distribution as in the past.

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

15. Suppose that the scores on a reading ability test are normally distributed with a mean of60 and a standard deviation of10. What proportion of individuals score at most42points on this test?

Round your answer to at least four decimal places.

16. The Diversity, Equity, and Inclusion (DEI) office of a major multinational bank is investigating the process used to make recent hires for financial analysts. The office knows that exactly10% of all applications were from minority candidates and that exactly8%of the open positions were filled by members of a minority.

For the investigation, the DEI office will take a random sample of900 applications. Letpbe the proportion of minority applicants in the sample.

Answer the following.

(a) Find the mean ofp

(b) Find the standard deviation ofp.

(c) Compute an approximation for P(p0.08), which is the probability that there will be fewer minority applicants in the sample than were hired by the bank. Round your answer to four decimal places.

17. A worldwide organization of academics claims that the mean IQ score of its members is115, with a standard deviation of16. A randomly selected group of40members of this organization is tested, and the results reveal that the mean IQ score in this sample is117.2 If the organization's claim is correct, what is the probability of having a sample mean of117.2 or less for a random sample of this size?

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

18. A researcher believes that about72%of the seeds planted with the aid of a new chemical fertilizer will germinate. He chooses a random sample of185seeds and plants them with the aid of the fertilizer. Assuming his belief to be true, approximate the probability that fewer than135of the185 seeds will germinate. Use the normal approximation to the binomial with a correction for continuity.

Round your answer to at least three decimal places. Do not round any intermediate steps

19. The Credit Risk Department of a major bank estimates the default rate on loans under$10,000 to be5%. A random sample of1900new loans that are under$10,000is going to be selected. Letpbe the proportion of defaults on the loans in the sample.

Answer the following.

(a)Find the mean ofp.

(b)Find the standard deviation ofp.

(c)Compute an approximation forPp0.06, which is the probability that6%or more of the loans in the sample will be defaulted on. Round your answer to four decimal places.

20. Suppose that a new treatment is successful in curing a common ailment 70% of the time. If the treatment is tried on a random sample of130 patients, approximate the probability that at least94 will be cured. Use the normal approximation to the binomial with a correction for continuity

Round your answer to at least three decimal places. Do not round any intermediate steps.