A 2005 Gallup Poll found that 7% of teenagers (ages 13 to 17) suffer from arachnophobia...

A 2005 Gallup Poll found that 7% of teenagers (ages 13 to 17) suffer from arachnophobia and are extremely afraid of spiders. At a summer camp there are 12 teenagers sleeping in each tent. Assume that these 12 teenagers are independent of each other.

(a) Calculate the probability that at least 4 of them suffers from arachnophobia.
(b) Calculate the probability that exactly 4 of them suffer from arachnophobia.
(c) Calculate the probability that at most 11 of them suffers from arachnophobia.

Solutions

Expert Solution

This is an example of binomial distribution because with teenagers only two outcomes are possible either they are scared of spiders or not. Also everyone's fear is independent of one another.

Since it is a discrete distribution we have to be careful with '<' and '=<'

(a) Calculate the probability that at least 4 (4 or more than 4) of them suffers from arachnophobia.

= 1 - [ P(X = 0 ) + P(X= 1)+ P(X = 2) + P(X = 3) ]

= 1 - (0.41886 + 0.37809 + 0.1565 + 0.03927)

(b) Calculate the probability that exactly 4 of them suffer from arachnophobia.

P(X = 4) =

= 1 - P(X = 12)

= 1 - 0

orchestra answered 1 year ago

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