Question

According to a recent survey, 75% of American households have a Vacuum Cleaner. If 20 American households are selected at random, find the probability that 18 of them have a Vacuum . Out of the selected households, what is the probability that there is more than 1 Vacuum? What is the probability out of the selected households, that there is at most 3 Vacuum ? |

Answer #1

Number of American households have a Vacuum Cleaner in random sample X ~ Binomial(n = 20, p = 0.75)

probability that 18 of them have a Vacuum = P(X = 18)

= 0.06694781

probability that there is more than 1 Vacuum = P(X > 1)

= 1 - P(X = 0) - P(X = 1)

= 1 - 0.0000 - 0.0000

= 1

probability out of the selected households, that there is at most 3 Vacuum = P(X 3)

= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= 0.0000 + 0.0000 + 0.0000 + 0.0000

= 0

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