True or false if the line y=2 is horizontal asymptote of y=f(x), then f is not defined at y=2

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

<h3>1. Michael Jordan Freethrow</h3>

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

<h3>2. Country Populations</h3>

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

<h3>3. Uninsured drivers</h3>

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