Statistical Applications Quiz 4

REAL EXAMPLE OF A STATISTICAL APPLICATIONS QUIZ 4

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Week Four Quiz

1. Please indicate whether each of the statements below is true or false.

a. A normal distribution is any distribution that is not unusual.

b. The graph of a normal distribution is bell-shaped.

c. If a population has a normal distribution, the mean and the median are not equal.

d. The graph of a normal distribution is symmetric.

Answer: Questions B and D are correct.

Using the 68-95-99.7 rule:

2. Assume that a set of test scores is normally distributed with a mean of 100 and a standard deviation of 20. Use the 68-95-99.7 rule to find the following quantities:

Suggest you make a drawing and label first…

a. Percentage of scores less than 100

50%

b. Relative frequency of scores less than 120

0.84

c. Percentage of scores less than 140

97.5%

d. Percentage of scores less than 80

16%

e. Relative frequency of scores less than 60

0.025

f. Percentage of scores greater than 120

16%

3. Assume the body temperatures of healthy adults are normally distributed with a mean of 98.20 °F and a standard deviation of 0.62 °F (based on data from the University of Maryland researchers).

a. If you have a body temperature of 99.00 °F, what is your percentile score?

90th percentile

b. Convert 99.00 °F to a standard score (or a z-score).

1.29

c. Is a body temperature of 99.00 °F unusual? Why or why not?

No, value lies less than 2 standard deviations from the mean.

d. Fifty adults are randomly selected. What is the likelihood that

the mean of their body temperatures is 97.98 °F or lower?

0.0065

e. A person’s body temperature is found to be 101.00 °F. Is the result unusual? Why or why not? What should you conclude?

The temperature is unusual. Lies more than 2 standard deviations above the mean.

f. What body temperature is the 95th percentile?

99.22

g. What body temperature is the 5th percentile?

97.18

h. Bellevue Hospital in New York City uses 100.6 °F as the lowest temperature considered to indicate a fever. What percentage of normal and healthy adults would be considered to have a fever? Does this percentage suggest that a cutoff of 100.6 °F is appropriate?

Fewer than 0.01%, and yes, it is appropriate.


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