need help on this hw question
Scuba-diving trips
The mailing list of an agency that markets scuba-diving trips to the Florida Keys contains 60% males and 40% females.
The agency calls 30 people chosen at random from its list.
What is the probability that 20 of the 30 are men?
Health Care: Flu Based on data from the Statistical Abstract of the United States, 112th Edition, only about 14% of senior citizens (65 years old or older) get the flu each year. However, about 24% of people under 65 years old get the flu each year. The general population consists of 12.5% senior citizens (65 years old or older).
(a) What is the probability that a person selected at random from the general population is a senior citizen who will get the flu this year?
(b)What is the probability that a person selected at random from the general population is a person under age 65 who will get the flu this year?
(c) Answer parts (a) and (b) for a community that has 95% senior citizens.
(d) Answer parts(a) and (b) for a community that has 50% senior citizens.
To find the probability that 20 of the 30 people selected are men, we can use the binomial probability formula. The formula is:
P(x) = C(n, x) * p^x * (1-p)^(n-x)
Where:
- P(x) is the probability of getting x successes
- C(n, x) is the number of combinations of n items taken x at a time
- p is the probability of success on a single trial
- n is the total number of trials
In this case, we want to find the probability of getting 20 men (x = 20) out of 30 people selected (n = 30). The probability of selecting a man from the list is p = 0.6 (given that 60% are males).
Now, let's plug in the values:
P(20) = C(30, 20) * 0.6^20 * (1-0.6)^(30-20)
To calculate C(30, 20), we use the formula for combinations:
C(n, x) = n! / (x! * (n-x)!)
C(30, 20) = 30! / (20! * (30-20)!)
Now, let's simplify and calculate:
C(30, 20) = 30! / (20! * 10!)
= (30 * 29 * 28 * ... * 21) / (20 * 19 * 18 * ... * 1)
After calculating C(30, 20), we can substitute all the values in the binomial probability formula and calculate P(20).
I hope this helps you understand how to approach and calculate the probability that 20 of the 30 selected people are men.