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national Bureau of statistics reported that approximately 30% of the population are unemployed. In conducting a random telephone surveys, what is the probability of getting two or fewer unemployed people in a sample of 20? “Binomial distribution”

User MatteKarla
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To solve this problem using the binomial distribution, we first need to identify the values of n, p, and x.

n = 20 (the sample size)
p = 0.30 (the probability of an individual being unemployed)
x = 0, 1, or 2 (the number of unemployed individuals we want to calculate the probability for)

Using the binomial probability formula, we can calculate the probability of getting 0, 1, or 2 unemployed individuals in a sample of 20:

P(X = 0) = (20 choose 0) * (0.30)^0 * (0.70)^20 = 0.0008
P(X = 1) = (20 choose 1) * (0.30)^1 * (0.70)^19 = 0.0069
P(X = 2) = (20 choose 2) * (0.30)^2 * (0.70)^18 = 0.0278

To get the probability of getting two or fewer unemployed people in the sample of 20, we add the probabilities of getting 0, 1, or 2:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0008 + 0.0069 + 0.0278 = 0.0355

Therefore, the probability of getting two or fewer unemployed people in a sample of 20 is approximately 0.0355 or 3.55%.
User Jurevert
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