1.Why the standard normal distribution is important in statistical analysis?

Many variables are normally distributed, and the distribution can be used to describe these variables.

2.Assume that the mean systolic blood pressure of normal adult is 120 mmHg and the standard deviation is 5.6. Assume the variable is normally distributed.

a.If an individual is selected, find the probability that the individual's blood pressure will be between 120 and 121.8 mmHg (Ans: 12.55%)

b.If a sample of 30 adults is randomly selected, find the probability that the individual's blood pressure will be between 120 and 121.8 mmHg. (Ans: 46.08%)

c.Why the answer to part a so much smaller than the answer to part b?

3.Proportions of prepared luncheon meats should have a pH values with a mean of 5.6 and a standard deviation of 1.0.The usual quality control procedure is to randomly sample each consignment of meat by testing the pH value of 25 portions.The consignment is rejected if the pH value of the sample mean exceeds 6.0.What is the probability of a consignment being rejected?Assume that the variable is approximately normally distributed.(Ans:0.0228)

4.A National survey of graduate students is conducted to assess their consumption of coffee. The following table summarizes the data:

Do not drink coffee

Drink Decaffeinated coffee Only

Drink caffeinated coffee

Total

Male

145

94

365

604

Female

80

121

430

631

Total

225

215

795

1235

a.What proportion of students drink decaffeinated coffee only?(Ans: 0.1741)

b.Among the coffee drinkers, men drink a mean of 3.2 cups per day with a standard deviation of 0.8 cups. Assume the number of cups per day follows a normal distribution.

i.What proportions drink 2 cups per day or more? (Ans: 0.9332)

ii.What proportions drink no more than 4 cups per day?( Ans: 0.8413)

iii.If the top 5% of coffee drinkers are considered "heavy" coffee drinkers, what is the minimum number of cups consumed by the heavy coffee drinkers? (Ans: cups)

iv.If a sample of 20 men is selected, what is the probability that the mean number of cups per day is greater than 3? (Ans: 0.8686)

5.Suppose that 10% of all persons are allergic to penicillin. What is the probability that less than 8% of persons in a sample of 1000 will be allergic to penicillin?

i.Calculate mean and standard deviation of the sampling distribution of this sample proportion. (ans: 0.1; 0.009)

ii.Comment on the shape of its sampling distribution.(Hint: Check for normality)

6.Suppose that 10% of all persons are allergic to penicillin. What is the probability that 7.5% to 9% of persons in a sample of 1000 will be allergic to penicillin? (Ans:0.1428)