Question

​24% of U.S. adults say they are more likely to make purchases during a sales tax holiday. You randomly select 10 adults. Find the probability that the number of adults who say they are more likely to make purchases during a sales tax holiday is​ (a) exactly​ two, (b) more than​ two, and​ (c) between two and​ five, inclusive

Answer 1

Explanation:

Use binomial probability:

P = nCr pʳ qⁿ⁻ʳ

where n is the number of trials,

r is the number of successes,

p is the probability of success,

and q is the probability of failure (1−p).

In this case, p = 0.24, q = 1−0.24 = 0.76, and n = 10.

a) P(r=2)

P = ₁₀C₂ 0.24² 0.76¹⁰⁻²

P = 0.288

b) P(r>2) = 1 − P(r=0) − P(r=1) − P(r=2)

P = 1 − (₁₀C₀ 0.24⁰ 0.76¹⁰⁻⁰) − (₁₀C₁ 0.24¹ 0.76¹⁰⁻¹) − (₁₀C₂ 0.24² 0.76¹⁰⁻²)

P = 1 − 0.064 − 0.203 − 0.288

P = 0.444

c) P(2≤r≤5) = P(r=2) + P(r=3) + P(r=4) + P(r=5)

P = (₁₀C₂ 0.24² 0.76¹⁰⁻²) + (₁₀C₃ 0.24³ 0.76¹⁰⁻³) + (₁₀C₄ 0.24⁴ 0.76¹⁰⁻⁴) + (₁₀C₅ 0.24⁵ 0.76¹⁰⁻⁵)

P = 0.288 + 0.243 + 0.134 + 0.051

P = 0.717