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 16 randomly observed individuals exactly 4 do not cover their mouth when sneezing?

(b)What is the probability that among 16 randomly observed individuals fewer than 5 do not cover their mouth when sneezing?

(c)Would you be surprised if, after observing 16 individuals, fewer than half covered their mouth when sneezing? Why?

Answer #1

Answer)

As there are fixed number of trials and probability of each and every trial is same and independent of each other

Here we need to use the binomial formula

P(r) = ncr*(p^r)*(1-p)^n-r

Ncr = n!/(r!*(n-r)!)

N! = N*n-1*n-2*n-3*n-4*n-5........till 1

For example 5! = 5*4*3*2*1

Special case is 0! = 1

P = probability of single trial = 0.267

N = number of trials = 16

R = desired success

A)

P(4) = 16c4*(0.267^4)*(1-0.267)^16-4 = 0.22251747806

B)

Fewer than 5

P(0) + P(1) + P(2) + P(3) + P(4) = 0.56847682269

C)

Fewer than half

Here P = 1 - 0.267 = 0.733 (as now they are asking fewer than half covered their mouth)

= P(0) + P(1) + .... P(7)

= 0.0117879153

When probability is less than 0.05

Then it is an unusual event

So yes i will be surprised

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 16 randomly observed individuals exactly 8
do not cover their mouth when sneezing? (b) What is the
probability that among 16 randomly observed individuals fewer than
6 do not cover their...

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 16
randomly observed individuals exactly 7do not cover their mouth
when? sneezing?
?(b) What is the probability that among 16
randomly observed individuals fewer than 5 do not cover their mouth...

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 18 randomly observed
individuals exactly 5 do not cover their mouth when sneezing?
(b) What is the probability that among 18 randomly observed
individuals fewer than 4 do not cover their...

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 10
randomly observed individuals exactly 4 do not cover their mouth
when? sneezing?
?(b) What is the probability that among 10
randomly observed individuals fewer than 5 do not cover their...

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. You sit on a bench in a mall and
observe people's habits as they sneeze.
What is the probability that among 10 randomly observed
individuals fewer than 4 do not cover their mouth when
sneezing?

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...

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 .267. Suppose you sit on a bench in a
mall and observe peoples habits as they sneeze.
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individuals exactly 6 do not cover their mouth when sneezing?
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