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
Answers
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.
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.
Round to four decimal places
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%.
Therefore, the probability that exactly 18 of the 22 searches used the Google search engine is approximately 0.0631 or 6.31%.