1) IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. LetX

=

X=

IQ of an individual.

(a) Find the z-score for an IQ of 121, rounded to three decimal places.1.400

Correct

(b) Find the probability that the person has an IQ greater than 121.0.08076

Correct

(c) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z-score. Use your z-score from part (a), rounded to one decimal place).

(d) MENSA is an organization whose members have the top 2% of all IQs. Find the minimum IQ needed to qualify for the MENSA organization.

(e) Sketch the graph, and write the probability statement.

(f) The middle 50% of IQs fall between what two values?

-

(g) Sketch the graph and write the probability statement.

2) The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10. Suppose that one individual is randomly chosen. LetX

=

X=

percent of fat calories.

(a) Find the z-score corresponding to 41 percent of fat calories, rounded to 3 decimal places.0.500

Correct

(b) Find the probability that the percent of fat calories a person consumes is more than 41.0.3085

Correct

(c) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z-score. Use your z-score from part (a), rounded to one decimal place).

(d) Find the maximum number for the lower quarter of percent of fat calories. Round your answer to 3 decimal places.29.300

Incorrect

(e) Sketch the graph and write the probability statement.

3) Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 21 days and a standard deviation of seven days.

(a) In words, define the random variable X.

(b) Find the z-score for a trial lasting 17 days.(Round your answer to three decimal places.)

(c) If one of the trials is randomly chosen, find the probability that it lasted at least 17 days.

(d) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z-score. Use your z-score from part (b), rounded to one decimal place).

(e) forty-one percent of all trials of this type are completed within how many days?

5) Suppose the systolic blood pressure (in mm) of adult males has an approximately normal distribution with mean

=125 and standard deviation

=14.

Create an empirical rule graph with the following:

• A title and label for the horizontal axis including units.
• Vertical lines for the mean and first 3 standard deviations in each direction with numerical labels on the horizontal axis
• Labels for the areas of the 8 regions separated by the vertical lines as well.

Note: This may be hand drawn or computer generated. See the models for desired formats.

a. Upload your completed file below.Question 1 Part 1 of 5

Choose FileNo file chosen

Now use your graph to answer the following questions.

b. About 95% of men will have blood pressure between what amounts?

and

c. What percentage of men will have a systolic blood pressure outside the range 83 mm to 139 mm?

d. Suppose you are a health practitioner and an adult male patient has systolic blood pressure of 170 mm. Use statistics to explain the gravity of his situation. Write an essay below that includes the following:

1. A brief description of the normal distribution.
2. Why the normal distribution might apply to this situation.
3. Describe the specific normal distribution for this situation (give the mean and standard deviation)
4. A brief description of the empirical rule
5. What region of the graph (drawn in part a) the individual falls in
6. An estimate of individual's percentile.
7. Why this signifies a health concern.
8. A suggested course of action.