Download WS 3.1 #3

Intro to Stats
3.1 Worksheet 3
Name __________________________________ Hour ________
NORMAL DENSITY CURVES
 I can use the properties of a normal density curve to sketch a normal distribution
1. In a normal distribution,
a. what percent of the data lies within 1 standard deviation of the mean?
b. what percent of the data lies within 2 standard deviations of the mean?
c. what percent of the data lies within 3 standard deviations of the mean?
2. List 5 properties of all normal curves:
 I can use the properties of a normal density curve to sketch a normal distribution
 I can use the Empirical Rule to calculate the probability of an event based on a normal distribution
3. The weights of bags of cookies are normally distributed, with a mean weight of 15 ounces and a standard
deviation of 0.085 ounce.
a. Sketch the normal curve of the bags of cookies’ weight:
b. Determine an interval of values into which 95% of the bags of cookies will fall:
c. The cookie company will not sell the cookie bags if their weights are more than 2 standard deviations
away from the average. What percent of the cookie bags would the company’s quality control turn away
because of weight?
d. If the cookie company makes 20,000 bags of cookies, how many bags will be sent back to repackage
because of weight?
4. The contents of a cereal box are normally distributed, with a mean weight of 20 ounces and a standard
deviation of 0.07 ounce.
a. Sketch the normal curve of the cereal box weights:
b.
Determine an interval of values into which 95% of cereal box weights will fall:
c. If the cereal company makes 150,000 boxes of cereal, how many bags will be within 1 standard deviation
of the mean?
d. What percent of the cereal box weights are above 20.14 ounces?
5. The weights of Chihuahuas are normally distributed, with a mean of 6.5 pounds and a standard deviation of 1.4
pounds.
a. Sketch a normal curve of the weights of Chihuahuas:
b. What is the interval of the middle 68% of the Chihuahua weights?
c. Some Chihuahuas get lazy living the life of luxury… what percent of the Chihuahuas weigh over 9.3 lbs?
d. One very handsome Chihuahua, Indigo Jones, weighs 7.2 pounds. How many standard deviations above the
average is he?
Intro to Stats
Name __________________________________ Hour ________
6. The systolic blood pressures of adults are normally distributed with a mean of 128.4 and a standard deviation
of 19.6
a. Sketch the normal curve for the blood pressures:
b. Give the interval in which blood pressures are approximately 68% of the population.
c. Give the interval in which 95% of the population falls
d. Give the interval in which 99.7% of the population falls
e. What is the percent of blood pressures above 148
f.
What is the percent of blood pressures below 89.2
7. The scores on a particular job aptitude test are normal with an average of 400 and a standard deviation of 100.
a. Sketch this distribution.
b. Shade the curve of the proportion of the population who scored in the top 2.5%
c. If a company will only consider those applicants scoring in the top 2.5%, what scores will they
consider?
8. The time to complete a certain loan application form is an average of 90 minutes with a standard deviation of
15 minutes.
a. Sketch this distribution:
b. What are the chances that the loan will take Less than 75 minutes?
c. What are the chances that the loan will take Between 90 and 120 minutes?
d. What are the chances that the loan will take More than 135 minutes?
9. The number of hours that the students in an Intro to Stats class watch the USA network (for NCIS and House
reruns of course) in a week is normally distributed with an average of 9 hours with a standard deviation of 2.5
hours.
a. Sketch the normal curve:
b. What percent of the students watch more than 11.5 hours of the USA network?
c. What percent of the students watch between 4 to 14 hours of the USA network?
d. One student watches 16.5 hours of the USA network a week. How many standard deviations over the
average are they?