The probability of an adverse reaction to a flu shot is 0.15. Let r be the numbe

Question

The probability of an adverse reaction to a flu shot is 0.15. Let r be the number of people suffering a reaction from a flu shot that has been given to a group of 6 people.

a.    Find P(r) for r = 0, 1, 2, 3, 4, 5, and 6.

The probability of an adverse reaction to a flu shot is 0.15. Let r be the number of people suffering a reaction from a flu shot that has been given to a group of 6 people.

b.   What is the expected number of people that will have an adverse reaction to the shot?

c.   Compute the standard deviation of the probability distribution.

The probability of an adverse reaction to a flu shot is 0.15. Let r be the number of people suffering a reaction from a flu shot that has been given to a group of 6 people.

d. Find P(2 or less have a reaction).

e. Find P(at least 3 people have a reaction).

Explanation / Answer

(a) P(flu shot adverse reaction) = 0.15

P(r) = 6Cr (0.15)r(0.85)6-r

b.   What is the expected number of people that will have an adverse reaction to the shot?

Expected Number of people = 0.15 * 6 = 0.90

(c) Compute the standard deviation of the probability distribution.

Std. deviation = sqrt (0.15 * 0.85 * 6) = 0.875

(d) Find P(2 or less have a reaction) = Pr(X = 0) + Pr(X = 1) + Pr(X = 2)

=  6C0 (0.15)0(0.85)6 +  6C1(0.15)1(0.85)5 +  6C2(0.15)2(0.85)4

= 0.3771 + 0.3993 + 0.1762 = 0.9526

(e) Pr(at least 3 people have a reaction) = Pr(X >= 3) = 1 - Pr(X < =2) = 1 - 0.9526 = 0.0474

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