Question

# Instructions: Write probabilities to four decimal places (percentages to two decimal places). Draw bell curves to...

Instructions: Write probabilities to four decimal places (percentages to two decimal places).

Draw bell curves to illustrate each desired areas. Use the correct probability notation (e.g. P(X

>12.5) = P(z > 1.2) …. Use the Standard Normal Distribution Table to answer Questions 1

& 8).

1. The total blood cholesterol levels in a certain Mediterranean population are found to be

normally distributed with a mean of 160 milligrams/deciliter (mg/dL) and a standard

deviation of 50 mg/dL. Researchers at the National Heart, Lung and Blood Institute

consider this pattern ideal for a minimal risk of heart attacks. [10 pts]

a) Find the percentage of this population who have blood cholesterol levels less than

150 mg/dL.

b. Find the percentage of this population who have blood cholesterol levels between

100 mg/dL and 200 mg/dL.

c. Find the percentage of this population who have blood cholesterol levels less than

150 mg/dL and more than 220 mg/dL.

d. Find the percentage of this population who have blood cholesterol levels which

exceed the ideal level by 20 mg/dL.

2. The length of human pregnancies from conception to birth varies according to a

distribution that is approximately normal with a mean of 266 days and standard deviation

16 days. [7 pts]

a. What is the probability that a pregnancy will last less than 270 days (about nine

months)?

b. What is the probability of pregnancies lasting between 240 and 270 days?

c. What is the probability of pregnancies lasting longer than 210 days?

3. The average length of a hospital stay for all diagnoses is 4.8 days. If we assume that the

lengths of hospital stays are normally distributed with a standard deviation of 1.45, then

30% of stays are less than how many days. [2 pts]

4. Assume that the mean systolic blood pressure of normal adults is 120 millimeters of

mercury (mm Hg) and the standard deviation is 5.6. Assume the variable is normally

distributed. [4 pts]

a. If an individual is selected, find the probability that the individual’s pressure will

be between 120 mm and 121.8 mm Hg.

b. If a sample of 30 adults is randomly selected, find the probability that the sample

mean will be between 120 mm and 121 mm Hg.

5. The American Red Cross reports that 45% of Americans have blood type O. We plan to

take a random sample of 1000 medical records. What is the probability that no more than

42% of the individuals in our sample would have blood type O? [3 pts]

6. At a local accounting firm, the mean fee for completing an individual’s tax return is \$225

with a standard deviation of \$28. Consider a random sample of 33 individual tax returns

from this firm. What is the probability that the mean amount billed for the sample differs

from the population mean by more than \$5? [4 pts]

7. At one private university, 34% are nursing majors. Suppose that 260 students are

randomly selected from a list in the registrar’s office. What is the probability that the

proportion of nursing students in the sample differs from the population proportion by

less than 2%? [4 pts]

8. In a famous research paper in the psychology literature, George Miller found that the

amount of information humans could process in short-term memory was 7 bits (pieces of

information), plus or minus 2 bits. Assume that the mean number of bits is 7 and the

standard deviation is 2, and that the distribution is normal. Suppose we take a sample of

100 people and test their short-term memory skills. [8 pts]

a. Find the probability that the sample mean number of bits retain in short-term

memory is greater than 7.5.

b. Find the probability that the mean number of bits retained in short-term memory

is less than 6.75.

c. Find the 97.5th percentile of the sample mean number of bits retained in shortterm memory