College Education and Business world success R. H. Bruskin Associates Market Research found that 40% of American do not think that having a college education is important to succeed in the business world. if a random sample of five Americans is selected, find these probabilities.
a) Exactly 2 people will agree with that statement.
b) At most 3 people will agree with that statement.
c) At least 2 people will agree with that statement.
d) Fewer than 3 people will agree with that statement.
To answer these probability questions, we need to use the binomial probability formula. The formula is:
P(x) = (nCx) * p^x * q^(n-x)
Where:
- P(x) is the probability of getting exactly x successes
- n is the number of trials (in this case, the number of people randomly selected)
- x is the number of successes (in this case, the number of people who agree with the statement)
- p is the probability of success (in this case, the proportion of Americans who do not think college education is important, which is 40% or 0.40)
- q is the probability of failure (in this case, the proportion of Americans who think college education is important, which is 60% or 0.60)
Now, let's solve each probability question step by step:
a) Exactly 2 people will agree with that statement.
Using the formula:
P(2) = (5C2) * (0.40)^2 * (0.60)^(5-2)
= (10) * (0.40)^2 * (0.60)^3
Solving this equation will give you the probability that exactly 2 people will agree with the statement.
b) At most 3 people will agree with that statement.
To calculate this probability, we need to sum the probabilities of getting 0, 1, 2, and 3 successes.
P(at most 3) = P(0) + P(1) + P(2) + P(3)
You can calculate each of the probabilities using the binomial probability formula as we did in question a.
c) At least 2 people will agree with that statement.
To calculate this probability, we need to sum the probabilities of getting 2, 3, 4, and 5 successes.
P(at least 2) = P(2) + P(3) + P(4) + P(5)
You can calculate each of the probabilities using the binomial probability formula.
d) Fewer than 3 people will agree with that statement.
To calculate this probability, we need to sum the probabilities of getting 0, 1, and 2 successes.
P(fewer than 3) = P(0) + P(1) + P(2)
You can calculate each of the probabilities using the binomial probability formula as we did in question a.
Remember, when using the binomial probability formula, always substitute the values accordingly to get the desired probability.