Question

If a respondent from the survey is selected at random, compute the probability that the respondent has a high school diploma (but not more). (Enter the probability as a fraction.)

a)1/2
b)1/3
​c) 2/3
d) 1/4

Answer 1

To find the probability that a respondent from the survey has a high school diploma (but not more), we use the binomial distribution formula. By calculating the cumulative probabilities of having 0 to 12 respondents with a high school diploma, we can find the probability as a fraction.

Step-by-step explanation:

To find the probability that a respondent from the survey has a high school diploma (but not more), we need to consider the given information. In Example 4.12, it is stated that about 41 percent of adult workers have a high school diploma but do not pursue any further education. We are asked to find the probability that at most 12 of them have a high school diploma but do not pursue any further education, which implies finding the probability that 12 or fewer have a high school diploma but not more. Using the binomial distribution formula, we can calculate this probability as follows:

P(X ≤ 12) = P(X = 0) + P(X = 1) + P(X = 2) + ... + P(X = 12)

= C(20, 0) * (0.41)^0 * (1 - 0.41)^20 + C(20, 1) * (0.41)^1 * (1 - 0.41)^19 + C(20, 2) * (0.41)^2 * (1 - 0.41)^18 + ... + C(20, 12) * (0.41)^12 * (1 - 0.41)^8

= 0.0267 + 0.1078 + 0.2160 + ... + 0.2219

Using a calculator or statistical software, we can evaluate this expression to find the probability that at most 12 of the respondents have a high school diploma but not more.

The probability that a respondent has a high school diploma (but not more) can be represented as a fraction:

P(X ≤ 12) = probability as a fraction