Approximately 75% of people eat pasta at least once each week. what is the probability that for a randomly selected group of 16 people more than half of the people will eat pasta at least once in any randomly selected week? (round to the nearest hundredth.)

the probability is 0.97

Step-by-step explanation:

We want to determine the probability that more than 8 people will eat pasta at least once in any randomly selected week. We would apply binomial distribution formula,

P(x = r) = nCr × q^(n-r) × p^r

Where p = probability of success = 75/100 = 0.75

q is probability of failure = 1 - q = 1 - 0.75 = 0.25

n = number of sample = 16

P(x greater than 8) = 1 - P(x ≤ 8)

P(x ≤ 8) = 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 = 0) = 16C0 × 0.25^(16-0) × 0.75^0 = 232.8 × 10^-12

P(x = 1) = 16C1 × 0.25^(16-1) × 0.75^1 = 0.00000001118

P(x = 2) = 16C2 × 0.25^(16-2) × 0.75^2 = 0.00000025146

P(x = 3) = 16C3 × 0.25^(16-3) × 0.75^3 = 0.0000035204

P(x = 4) = 16C4 × 0.25^(16-4) × 0.75^4 = 0.00003432389

P(x = 5) = 16C5 × 0.25^(16-5) × 0.75^5 = 0.00024713203

P(x = 6) = 16C6 × 0.25^(16-6) × 0.75^6 = 0.00136

P(x = 7) = 16C7 × 0.25^(16-7) × 0.75^7 = 0.0058

P(x = 8) = 16C8 × 0.25^(16-8) × 0.75^8 = 0.0197

P(x ≤ 8) = 0.027

P(x greater than 8) = 1 - 0.027 = 0.97

step-by-step explanation:

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