Question

1.Famous basketball player Michael Jordan had a free throw percentage of 0.83. (He made 83% of his free throw shots.) Assume that each free throw shot is independent. Show your work. Part A: What is the probability that the next free throw he misses will be the 6th throw? Round your answer to 4 decimal places. (5 points) Part B: What is the expected number of free throws until he misses his first free throw shot?
2.The 20 most populous countries in the world have an average population of 268.35 million with a standard deviation of 370.43 million. The United States has a population of 332 million, Egypt has a population of 104 million, and Mexico has a population of 128 million. India has a z-score of 2.86 , Japan has a z-score of -0.39, and Brazil has a z-score of -0.15. Part A: Calculate the z-scores for the United States, Egypt, and Mexico. Show your work. (6 points) Part B: List all 6 countries in order from smallest to largest population and then explain why you ranked them this way. No explanation = no credit

3. It is estimated that 12.6% of drivers are uninsured.

Part A: What is the probability that exactly 5 drivers are uninsured if a police officer pulls over 30 drivers? Round your answer to 4 decimal places. Show your work. (5 points)

Part B: What is the probability the next uninsured driver that the police officer pulls over is the 7th driver?

Answer 1

Michael Jordan's Freethrow, the population of the 6 countries and the distribution of the uninsured drivers are illustrations of probabilities

1. Michael Jordan Freethrow

The given parameter is:

p = 83% -- the percentage of free throws he made

Probability that he misses his 6th throw

The probability that he misses his 6th throw is:

P = P(He made the first 5 throws) * P(He lost the 6th)

This gives

P = (83%)^5 * (1 - 83%)^1

P = 0.0670

Expected number of miss

The expected number till he misses the first free throw is:

E(x) = np

This gives

E(x) = 6 * 83%

E(x) = 4.98

Approximate

E(x) = 5

Hence, the probability that he misses his 6th throw is 0.0670 and the expected number till he misses the first free throw is 5

2. Country Populations

The given parameters are:

Average population = 268.35 million

Standard deviation = 370.43 million

The z-scores for the United States, Egypt, and Mexico

This is calculated as:

z = (x - $\mu$)/$\sigma$

So, we have:

US = (332 million - 268.35 million)/ 370.43 million

US = 0.17

Egypt = (104 million - 268.35 million)/ 370.43 million

Egypt = -0.44

Mexico = (128 million - 268.35 million)/ 370.43 million

Mexico = -0.38

The countries from the smallest to the largest

By comparing the z-score of the countries, the order of the countries are:

Egypt, Japan, Mexico, Brazil, United States and India

The countries are ranked that way because the higher the z-score, the higher the population

3. Uninsured drivers

The given parameter is:

p = 12.6% -- the percentage of uninsured drivers

Probability that exactly 5 drivers of 30 are uninsured

This is calculated as:

P(x) = nCx * p^x * (1 - p)^(n-x)

So, we have:

P(5) = 30C5 * (12.6%)^5 * (1 - 12.6%)^(30-5)

Evaluate the product

P(5) = 0.1561

Probability that the next uninsured driver is the 7th

This is calculated as:

P = P(First 6 are insured) * P(7th is unisured)

This gives

P = (1 - 12.6%)^6 * (12.6%)^1

P = 0.0562

The probability that exactly 5 drivers of 30 are uninsured is 0.1561, and the probability that the next uninsured driver is the 7th is 0.0562

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