According to a study done by a university? student, the probability a randomly s
ID: 3372155 • Letter: A
Question
According to a study done by a university? student, the probability a randomly selected individual will not cover his or her mouth when sneezing is 0.267.
Suppose you sit on a bench in a mall and observe? people's habits as they sneeze.
?(?a)
What is the probability that among
12
randomly observed individuals exactly
6
do not cover their mouth when? sneezing?
?(?b)
What is the probability that among
12
randomly observed individuals fewer than
5
do not cover their mouth when? sneezing?
?(?c)
Would you be surprised? if, after observing
12
?individuals, fewer than half covered their mouth when? sneezing? Why?
?(?a)
The probability that exactly
6
individuals do not cover their mouth is
0.0220.
?(Round to four decimal places as? needed.)
?(?b)
The probability that fewer than
55
individuals do not cover their mouth is
nothing .
?(Round to four decimal places as? needed.)
?(?c)
This
would
would not
would
be surprising because the probability of observing fewer than half covering their mouth when sneezing is
nothing ?,
which
is
is
is not
an unusual event.
?(Round to four decimal places as? needed.)
Explanation / Answer
X ~ Binomial (n,p)
Binomial probability distribuion is
P(X) = nCx px ( 1 - p)n-x
a)
n = 12 , p = 0.267 , x = 6
P( X = 6) = 12C6 0.2676 0.7336
= 0.0519
b)
P( X < 5) = P( X <= 4)
= P( X = 0) +P( X = 1) +P( X = 2) +P( X = 3) +P( X = 4)
= 12C0 0.2670 0.73312 +12C1 0.2671 0.73311 +12C2 0.2672 0.73310 +12C3 0.2673 0.7339 +12C4 0.2674 0.7338
= 0.8053
c)
P( individual covered their mouth when sneezing) = 1 - 0.267 = 0.733
P( X < 6) = P( X <= 5)
= P( X = 0) +P( X = 1) +P( X = 2) +P( X = 3) +P( X = 4) +P( X = 5)
= 12C0 0.7330 0.26712 +12C0 0.7331 0.26711 +12C2 0.7332 0.26710 +12C3 0.7333 0.2679 +
12C4 0.7334 0.2678 + 12C5 0.7335 0.2675
= 0.0206
We would surprised if less than half of the 12 covered their mouth when sneezing since probability is
less than 0.05.
Since probability is less than 0.05, it is unusual event.
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