Question

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

Answer #1

In a recently released report, the total blood cholesterol
levels for adult Americans is an average of 191 mg/dL with a
standard deviation of 11.8 mg/dL.
13. Find the percentage of the population with a cholesterol
reading of less
than 190
mg/dL.
14. Find the percentage of the population with a cholesterol
reading of more
than 195
mg/dL.
15. Find the percentage of the population with a cholesterol
reading between
185 and 195 mg/dL.
16. Find the percentage...

According to a recent poll cholesterol levels in healthy adults
are skewed right with a mean of 209 mg/dL and a standard deviation
of 35 mg/dL. A random sample of 42 healthy adults is selected. Find
the probability that the total cholesterol level in the sample of
42 adults will be less than 8400.
a. 0.0475
b. 0.9525
c. 1
d. 0
e. 0.3974

Total cholesterol levels for women under 30 in Podunk are
normally distributed with mean 173 mg/dL and standard deviation
27.2 mg/dL.
a. If a woman is selected at random, find the probability that
her total cholesterol is higher than 180 mg/dL.
b. What cholesterol levels make up the top 70% of this
distribution?

Too much cholesterol in the blood increases the risk of heart
diseases. Young women are generally less afflicted with high
cholesterol than other groups. The cholesterol levels for women
aged 20 to 34 follow an approximately normal distribution with mean
190 milligrams per deciliter (mg/dl) and standard deviation 41
mg/dl.
(a) Cholesterol levels above 270 mg/dl demand medical attention.
What percent of young women have levels above 270 mg/dl?
(b) Levels above 220 mg/dl are considered borderline high. What
percent...

We want to compare fasting serum cholesterol levels of Filipino
women to that of the other foreign women. Assume the cholesterol
levels in 20- to 39-years old women in other foreign countries is
normally distributed with mean µ = 190 mg/dl. Blood tests are
performed on 100 female Filipinos in this age range rendered a
sample mean cholesterol level of 181.52 mg/dl and standard
deviation of 40 mg/dl. Conduct a test of hypothesis to determine
whether Filipino women have lower...

The length of a women's pregnancies are normally distributed
with a population mean of 266 days and a population standard
deviation of 16 days.
a. What is the probability of a randomly selected pregnancy
lasts less than 260 days?
b. A random sample of 20 pregnancies were obtained. Describe the
sampling distribution of the sample mean length of pregnancies (eg.
Is it approximately normally distributed? Why or why not? What are
the mean and standard deviation?
c. What is the...

1. Write the corresponding letter of the distribution used to
conduct the test to answer the question or to find the probability
requested in the blank to the left of the given information. You
will only use each letter once.
a. Student’s T
b. Standard Normal
c. Chi-Square
d. Binomial
e. Poisson
_________________Suppose that a doctor claims that 17 year olds
have an average body temperature that is warmer than the commonly
accepted average human temperature of µ = 98.6...

In a test of the effectiveness of garlic for lowering
cholesterol, 49 subjects were treated with garlic in a processed
tablet form. Cholesterol levels were measured before and after the
treatment. The changes (before minus after) in their levels of
LDL cholesterol (in mg/dL) have a mean of 3.9 and a standard
deviation of 19.1. Construct a 99% confidence interval estimate of
the mean net change in LDL cholesterol after the garlic treatment.
What does the confidence interval suggest about...

Suppose we want to compare fasting serum-cholesterol
levels among recent Chinese immigrants to Ghana with typical levels
found in the general Ghanaian population. Suppose we assume
cholesterol levels in women ages 21−40 in Ghana are approximately
normally distributed with mean 190 mg/dL. It is unknown whether
cholesterol levels among recent Chinese immigrants are higher or
lower than those in the general Ghanaian population. Let’s assume
that levels among recent female Chinese immigrants are normally
distributed with unknown mean μ. Hence...

In a test of the effectiveness of garlic for lowering
cholesterol, 44 subjects were treated with garlic in a processed
tablet form. Cholesterol levels were measured before and after the
treatment. The changes in their levels of LDL cholesterol (in
mg/dL) have a mean of 3.5 and a standard deviation of 19.7.
Complete parts (a) and (b) below. a. What is the best point
estimate of the population mean net change in LDL cholesterol after
the garlic treatment? The best...

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