2. We are interested in analyzing data related to car accidents, age, and gender

Question

2. We are interested in analyzing data related to car accidents, age, and gender. Use U to denote under 21 years old and M to denote Male. The probability that someone gets in a car accident and is under 21 years old is 21%. The probability that someone gets in a car accident and is male is 67%. The probability that they get in a car accident and are a male under the age of 21 is 14%.

a. What percentage of people get in a car accident and are under the age of 21 or male?

b. What percentage of people get in a car accident and are not male?

c. Given someone is under the age of 21, what is the probability they are also male?

d. What percentage of people get in a car accident and are not under the age of 21 nor male?

e. Are U and M mutually exclusive events? Why or why not?

f. Are U and M independent events? Explain, using probabilities.

g. If we know someone is Male, what is the probability they are also under the age of 21?

3. Similarly to #2, we know that 7% of car accidents happen in January. Suppose we take a sample of 30 car accidents.

h. How many car accidents out of the 30 are expected to happen in January?

i. What is the standard deviation?

j. What is the probability that exactly 2 of the car accidents happen in January?

k. What is the probability that more than 2 of the car accidents happen in January?

Suppose we go back to the example from question 3. Suppose the probability remains at 7% but we now take a sample of size 200.

l. What is the standard error of the proportion?

m. What is the probability that the sample proportion of car accidents that happen in January will be between 5% and 10%?

Explanation / Answer

a) 14% of people get in a car accident under 21 year old male

b) 33% of people get in car accident are not male

c) 0.21 is probability that someone is under age 21

d) 86% of people get in car accident are not male nor age under 21.

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