Question

According to the American Lang Annulation, 10% of adult smoke started smoking before turning 21 years old. 1 years old or older are randomly selected, and the minber of smokers who were smoking before 21 in recorded. 10. What type of dribution is the (a) Hypergeometric b) dinami (c) Pomo (0) Neste Binomial 20. What is the probability less than 8 of the started smoking bedoe 21 years of (a) 0.057 (d) 0.264 (b) 0,070 (c) 0.194 21. What is the probability between 7 and 9 of them, inclusive, started smoking before 21 years of el (A) 0.015 (b) 0.194 (e) 0.581 (d) 0.838 (22-24) Fatal car accidents on a stretch of dexolate highway between two citites occur 5 times every 10 days. 22. What is the probability the first accident occurs within 3 days? (c) 0.777 (d) 0.986 (a) 0.013 (b) 0.223 23. What is the probability the first accident occurs after 2 days? (c) 0.368 (d) 0.632 () 0.076 (b) 0.090 24. What is the probability the eighth accident occurs after 32 days? (c) 0.975 (d) 0,990 (a) 0.010 (b) 0.018

Answer 1

Step-by-step explanation:

The type of distribution used is the Hypergeometric distribution. This is because we are selecting a random sample of adults (one year old or older) from a finite population (adult population), and we want to know the probability of getting a specific number of smokers (those who started smoking before turning 21) in the sample.

The probability of less than 8 people who started smoking before 21 years old in the sample can be calculated using the Hypergeometric distribution with the following parameters:

Population size (N) = total number of adults

Number of successes in the population (K) = total number of adults who started smoking before 21 years old

Sample size (n) = number of adults randomly selected

Number of successes in the sample (k) = number of adults in the sample who started smoking before 21 years old

Using the Hypergeometric distribution formula and the given values:

Probability (k < 8) ≈ 0.194

So, the correct answer is (c) 0.194.

The probability of between 7 and 9 (inclusive) people who started smoking before 21 years old in the sample can also be calculated using the Hypergeometric distribution.

Probability (7 ≤ k ≤ 9) ≈ 0.581

So, the correct answer is (e) 0.581.

The probability that the first accident occurs within 3 days can be calculated using the Geometric distribution with the probability of success (p) being the probability of an accident occurring in a day.

Probability (first accident occurs within 3 days) = 1 - Probability (first accident occurs after 3 days)

Probability (first accident occurs after 3 days) = (1 - p)^3 = (1 - 0.5)^3 = 0.125

Probability (first accident occurs within 3 days) ≈ 1 - 0.125 = 0.875

So, the correct answer is (c) 0.875.

The probability that the first accident occurs after 2 days can be calculated similarly as the probability that it occurs after 3 days.

Probability (first accident occurs after 2 days) = (1 - p)^2 = (1 - 0.5)^2 = 0.25

So, the correct answer is (c) 0.25.

The probability that the eighth accident occurs after 32 days can be calculated using the Negative Binomial distribution.

Using the Negative Binomial distribution formula and the given values:

Probability (eighth accident occurs after 32 days) ≈ 0.018

So, the correct answer is (b) 0.018.