Exercises. 1. For a population, N =40 000 and p = 0.65, find the Z value for each of the following for n= 200

1. For a population, N =40 000 and p = 0.65, find the Z value for each of the following for n = 200

a) =0.59; b) =0.72; c) =0.43; d) =0.73

2. 83% of the households of a large city own VCRs. Let be the population of the households who own VCRs in a random sample of 400 households. Find the probability that the value of will be

a) between 0.85 and 0.88

b) more than 0.80

3. A doctor believes that 80% of all patients having a particular disease will be fully recovered within 3 days after receiving a new drug. Assume that a random sample of 230 patients is selected.

a) What is the mean of the sample proportion of patients?

b) What is the variance of the sample proportion?

c) What is the standard error (standard deviation) of the sample proportion?

d) What is the probability that the sample proportion is less than 0.75?

e) What is the probability that the sample proportion is between

0.78 and 0.85?

4. Sixty percent of adults favor some kind of government control on the prices of medicines.

a) Find the probability that the proportion of adults in a random sample of 200 who favor some kind of government control on the prices of medicines is

i) less than 0.55; ii) between 0.57 and 0.68.

b) What is the probability that the proportion of adults in a random sample of 200 who favor some kind of government control is within 0.04 of the population proportion?

c) What is the probability that the sample proportion is greater than the population proportion by 0.06 or more?

5. Stress on the job is a major concern of a large number of people who go into managerial positions. Eighty percent of all managers of companies suffer from stress. Let be the proportion in a sample of 100 managers of companies who suffer from stress.

a) What is the probability that this sample proportion is within 0.08 of the population proportion?

b) What is the probability that this sample proportion is not within 0.08 of the population proportion?

c) What is the probability that this sample proportion is lower than the population proportion by 0.10 or more?

d) What is the probability that this sample proportion is greater than the population proportion by 0.11 or more?

6. A private university has 1250 students. Of these, 357 concerned about the GPA. A random sample of 265 students was taken.

a) What is the standard error (standard deviation) of the sample proportion of students who are concerned about the GPA?

b) What is the probability that the sample proportion is less than 0.35?

c) What is the probability that the sample proportion is between

0.25 and 0.33?

7. A plant has total of 736 employees. Of these, 342 are married. A random sample of 170 employees was taken.

a) What is the mean of the sample proportion of married employees?

b) What is the standard error of the sample proportion of married employees?

c) What is the probability that the sample proportion is greater than 0.37?

d) What is the probability that the sample proportion is between

0.43 and 0.53?

8. Suppose that 78% of all adults like sport.

a) Find the probability that the proportion of adults who like sport in a random sample of 400 is

i) more than 0.81; ii) between 0.75 and 0.82

iii) less than 0.80; iv) between 0.73 and 0.76

b) What is the probability that the proportion of adults in a random sample of 400 who like sport is within 0.05 of the population proportion?

c) What is the probability that the proportion of adults in a random sample of 400 who like sport is lower than the population proportion by 0.04 or more?

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