Question

According to a recent report, 65% of Internet searches used the Google search engine. Assume that a sample of 22 searches are studied. What's the probability that Exactly 18 of them used the Google search engine

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the probability that exactly 18 searches used the Google search engine out of a sample of 22, we can use the binomial probability formula:

P(x) = (nCx) * (P^x) * ((1-P)^(n-x))

Where:
n = 22 (number of searches studied)
x = 18 (number of searches using Google)
P = 0.65 (probability of using Google)
1-P = 0.35 (probability of not using Google)

Plugging in the values:

P(18) = (22C18) * (0.65^18) * (0.35^(22-18))

P(18) = (22! / 18!(22-18)!) * (0.65^18) * (0.35^4)

P(18) = (22! / 18!4!) * (0.65^18) * (0.35^4)

P(18) = (7315) * (0.0035) * (0.0021)

P(18) = 0.054 (rounded to 3 decimal places)

Therefore, the probability that exactly 18 of the 22 searches used the Google search engine is approximately 0.054.

Answer 2

Round to four decimal places

Answer 3

[AI-generated answer — Bot GPT 3.5]

P(18) = 0.0631

Therefore, the probability that exactly 18 of the 22 searches used the Google search engine is approximately 0.0631 or 6.31%.