1. A student knows they need to get 8 questions out of 10 correct on a final quiz in order to keep an A in the class. How many different combinations of 7 questions could they answer correctly out of the 10?
2. Use R to denote brown eyes, L to denote Blue eyes, and B to denote blonde hair. Based on prior information, we know that roughly 32% of people have blue eyes and 33% of people have brown eyes. 45% of people have blue eyes and blonde hair, whereas only 7% of people have brown eyes and blonde hair. We also know that 50% of people have brown eyes or blonde hair.
a. What percentage of people are blonde?
b. What percentage of people do NOT have blue eyes or blonde hair?
c. Are R and L mutually exclusive events? Why or why not?
d. Are R and B mutually exclusive events? Why or why not?
e. Are R and L independent? Explain, using probabilities.
f. Are L and B independent? Explain, using probabilities.
g. If we know someone has Brown eyes, what is the probability that they are also blonde?
3. Similarly to #2, we know that 12% of people have green eyes. Suppose we take a sample of 25 people.
a. How many adults are expected to have green eyes in the sample of 25?
b. What is the standard deviation?
c. What is the probability that exactly 2 people in the sample will have green eyes?
d. What is the probability that more than 2 of people in the sample will have green eyes?
4. The following information was gathered from 159 different beers. Each one had their percent alcohol recorded and the following frequencies were found:
Percent Alcohol |
Frequency |
2 |
2 |
3 |
4 |
4 |
80 |
5 |
46 |
6 |
10 |
7 |
7 |
8 |
5 |
9 |
3 |
10 |
1 |
11 |
1 |
a. Find the average percent alcohol for these 159 types of beers.
b. Find the standard deviation of this distribution.
5. Assume the distribution of minutes spent exercising per week is Normal. We know from past information that the average amount of minutes spent exercising per week is 175 with a standard deviation of 184 minutes. Suppose we take a sample of 200 people.
a. What is the probability that a randomly selected person will exercise more than 420 minutes per week, averaging an hour per day?
b. What is the probability that a randomly selected person will exercise less than 210 minutes per week, which equates to the 30 minutes per day suggested by healthcare professionals?
c. What is the probability that a randomly selected person will put in between an hour and three hours per week?
d. What is the probability that the average amount of exercise per week per person in our sample of 200 will be more than 210 minutes per week? (Meaning that on average, they exercise more than the recommended minimum amount).
e. What amount of minutes defines the lowest 24.2% of the distribution for an individual person?
f. What amount of minutes defines the highest 7.93% of the distribution for an individual person?
6. Suppose we go back to the example from question 3. Suppose the probability remains at 12% but we now take a sample of 50 people.
a. What is the standard error of the proportion?
b. What is the probability that the sample proportion of people with green eyes will be between 5% and 20%?
7. Two estimates are available for the same population parameter. Estimate one has a standard deviation of 2.7 and estimate two has a standard deviation of 2.5. Estimate two is not consistent, whereas estimate one is consistent. Which estimate would you choose and why?
8. Suppose I have a large group of students to survey from. I decide to divide them up based on majors and then randomly sample from within each major. This is an example of which sampling method?