According to a survey, 2323% of residents of a country 25 years old or older had earned at least a bachelor's degree. You are performing a study and would like at least 1010 people in the study to have earned at least a bachelor's degree. (a) How many residents of the country 25 years old or older do you expect to randomly select? (b) How many residents of the country 25 years old or older do you have to randomly select to have a probability 0.9450.945 that the sample contains at least 1010 who have earned at least a bachelor's degree? (a) The number of randomly selected residents is 4444. (Round up to the nearest integer.) (b) The number of randomly selected residents, with a probability 0.9450.945 containing at least 1010 who have earned at least a bachelor's degree, is 2828. (Round up to the nearest integer.)

a) 44

b) 64

Step-by-step explanation:

Applying the central limit theorem, the proportion of the random sample of 25 years old or older that have earned at least a bachelor's degree will be equal to the population proportion of 23%.

Mean = np

Mean = 10

p = 0.23

n = ?

10 = n×0.23

N

n = (10/0.23) = 43.5 = 44 to the nearest whole number.

b) This is a binomial distribution problem with the probability known and the number of trials unknown.

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = ?

x = Number of successes required = 10

p = probability of success = 0.23

q = probability of failure = 1 - 0.23 = 0.77

P(X ≥ 10) = 0.945

P(X ≥ 10) = 1 - P(X < 10) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9)]

0.945 = 1 - [Σ P(X=x)] (with the summation of x from 0 to 9)

Using the trial and error method on the binomial distribution formula calculator, n is obtained to be 64.

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step-by-step explanation:

the correct answer is x/3+10≥32

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