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Arachnophobia. A 2005 Gallup Poll found that 7% of
Chapter , Problem 3.32(choose chapter or problem)
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 10 teenagers sleeping in each tent. Assume that these 10 teenagers are independent of each other.
(a) Calculate the probability that at least one of them suffers from arachnophobia.
(b) Calculate the probability that exactly 2 of them suffer from arachnophobia.
(c) Calculate the probability that at most 1 of them suffers from arachnophobia.
(d) If the camp counselor wants to make sure no more than 1 teenager in each tent is afraid of spiders, does it seem reasonable for him to randomly assign teenagers to tents?
Questions & Answers
QUESTION:
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 10 teenagers sleeping in each tent. Assume that these 10 teenagers are independent of each other.
(a) Calculate the probability that at least one of them suffers from arachnophobia.
(b) Calculate the probability that exactly 2 of them suffer from arachnophobia.
(c) Calculate the probability that at most 1 of them suffers from arachnophobia.
(d) If the camp counselor wants to make sure no more than 1 teenager in each tent is afraid of spiders, does it seem reasonable for him to randomly assign teenagers to tents?
ANSWER:
Step 1 of 5
To solve this problem, we will use the binomial probability formula, which is appropriate when there are two possible outcomes (success or failure) for each individual and the events are independent.
In the given case, success is defined as a teenager suffering from arachnophobia, and failure is defined as a teenager not suffering from arachnophobia.
Probability of success (p) = 7% or 0.07 (the proportion of teenagers with arachnophobia).
The probability of failure is
\(q = 1 - p\)
\(= 1 - 0.07\)
\(= 0.93\)
Number of trials (n): 10 teenagers in each tent.
Let “A” denote a teenager suffering from arachnophobia.
The pmf of binomial distribution is: \(P\left( {X = x} \right) = {}^n{C_x}{p^x}{\left( {1 - p} \right)^{n - x}}\)