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Math 100

Worksheet for Lesson 14

Name: _____________________________

Date: ____________________

1. Suppose that the weights of newborn babies are normally distributed with the mean of 3200

grams and standard deviation of 300 grams. Princess Charlotte was born in May 2015 weighing

3700 grams.

a. What weight has the z-score of 0? How about the z-score of 1.0?

b. What is the z-score of Princess Charlotte’s weight?

c. What % of the babies are born weighing less than Princess Charlotte? (This shows the

“percentile” of her weight.)

2. Suppose you bought a 2-liter bottle of Coke, but you observed that there was only 1.95 liters of

Coke when you measured the volume carefully. Assume that the volumes in a 2.0-leter bottle is

normally distributed with the mean of 2.05 and standard deviation of 0.05 liter.

a. What is the z-score corresponding to 2.0 liters? How about 2.05 liters?

b. What is the probability that any given bottle has at least 1.95 liters?

c. Why do you think the company will have a mean of 2.05 liters when they advertise it as

a 2-liter bottle?

______________________________________________________________________

The standard normal distribution is a function of 𝑧 so that the total area under the curve is 1. This is extensively studied and

universally used in statistics. Here is the formula:

1 2

1

𝑓(𝑧) =

𝑒 −2𝑧

√2𝜋

The Normal Distribution is even more important because of what is known as the Central Limit Theorem.

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Math 100

Worksheet for Lesson 12

Name: _____________________________

Date: ____________________

1. Suppose you want to find the average household income in America. So you pick 10 households

from each state (a total of 500 households) and find their income.

a. What is the population? What is the parameter you want to find?

b. What type of data is this?

c. What is the sample? How big is your sample? What method of sampling was used?

d. What type of study is this? Is this a good method for this study?

e. Suppose the average income of the 500 households was $52,000. What is this value?

Does it accurately estimate the real average household income in America?

2. You want to know the political affiliations of all the students at your college, and you have a list

of every student enrolled. You plan to ask 1000 of them their political affiliation (party). How

would you get the 1000 students for your sample under

i. Random sampling?

ii. Convenience sampling?

iii. Systematic sampling?

iv. Stratified (quota) sampling?

3. A study is conducted to show that a new fish oil product prevents heart diseases.

a. What type of study is this? Can a placebo be used?

b. Is a single-blind test appropriate? How about a double-blind test?

4. It is discovered that those who jog 30 minutes a day live longer. Can you conclude that jogging

causes people to live longer based on this study?

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Math 100

Worksheet for Lesson 13

Name: _____________________________

Date: ____________________

1. A sample of seven test scores in a recent physics exam: 30, 40, 70, 70, 85, 95, 100.

a. Find the mean, median, and mode.

b. Find the range.

c. Find the standard deviation.

2. Someone studied the waiting time at two different coffee shops. They had the same mean

waiting time (4.8 minutes), but the standard deviation was 1.3 minutes at Café A and 2.5

minutes at Café B. Which one would you prefer to go to? Why?

3. In a 1997, a study was conducted to see what private high school in America had graduates with

the highest income. A school called Lakeside High School in Seattle won first place, with the

average graduate earning more than $2.5 million. How could this happen?

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Math 100

Worksheet for Lesson 11

Name: _____________________________

Date: ____________________

1. There is a game involving three coin tosses. Suppose you get $6 if you get thee Tails but lose $2

otherwise. Would you play this game? Why or why not? Write your reason using the term

“expected value.”

2. You are asked to create a four-digit PIN (using numerals 0 through 9).

a. Does the order matter? (Is the order relevant?)

b. How many possible PINs are there?

c. How many PINs are possible if no digits can be repeated?

d. How many PINs are there if the first digit cannot be 0?

3. You have ten books you want to take on your plane trip, but due to weight limitations, you can

only take 3.

a. How many reading lists of 3 books can you create if the order is important?

b. In how many ways can you just pick 3 books if the order is not important?

c. In how many ways can you choose 7 books you are leaving at home? (The order is

clearly irrelevant.)

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Normal Distribution

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