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Seventy-five percent of consumers prefer to purchase electronics online. You randomly select 8 consumers. Find the probability that the number of consumers who prefer to

purchase electronics online is (a) exactly five, (b) more than five, and (c) at most five.

(a) Find the probability that the number that prefer to purchase electronics online is exactly five.

P(5)=

(Round to three decimal places as needed.)

Sagot :

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Using the binomial probability relation, the probability of the following events are :

  • P(x = 5) = 0.2076
  • P(x > 5) = 0.6785
  • P(x ≤ 5) = 0.3215

Using the relation :

P(x = x) = nCx * p^x * q^(n-x)

  • Probability of success, p = 0.75
  • q = 1 - p = 1 - 0.75 = 0.25
  • Number of trials, n = 8

Probability of exactly 5 :

P(x = 5) = 8C5 × 0.75^5 × 0.25^3

P(x = 5) = 0.2076

2.) Probability of selecting more than 5 :

P(x > 5) = p(6) + p(7) + p(8)

Using a binomial probability calculator :

P(x > 5) = 0.6785

3.)

Probability at most 5 :

P(x ≤ 5) = p(0) + p(1) + p(2) + p(3) + p(4) + p(5)

Using a binomial probability calculator :

P(x ≤ 5) = 0.3215

Therefore, the probability of selecting at most 5 is 0.3215

Learn more :https://brainly.com/question/12474772

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