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Sagot :
Answer: 0.6274
Step-by-step explanation:
Given: The proportion of patients experience injection-site reactions with the current needle : p=0.11
Sample size : n= 4
Let x be a binomial random variable that represents the people get an injection-site reaction.
Binomial probability formula: [tex]P(X=x)= ^nC_x p^x(1-p)^{n-x}[/tex]
The required probability : P(x=0)
[tex]=\ ^4C_0(0.11)^0(1-0.11)^4\\\\=(1)(1)(0.89)^4\\\\=0.62742241\\\approx0.6274[/tex]
Hence, the probability that none of the 4 people get an injection-site reaction = 0.6274
The probability that none of the 4 people get an injection-site reaction would be 0.6274.
How to find that a given condition can be modelled by binomial distribution?
Binomial distributions consists of n independent Bernoulli trials.
Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))
Suppose we have random variable X pertaining to binomial distribution with parameters n and p, then it is written as
[tex]X \sim B(n,p)[/tex]
The probability that out of n trials, there'd be x successes is given by
[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]
A medical device company knows that 11% of patients experience injection-site reactions with the current needle.
If 4 people receive injections with this type of needle.
The proportion of patients who experience injection-site reactions with the current needle
p=0.11
Sample size : n= 4
Let a binomial random variable be x that represents the people who get an injection-site reaction.
Binomial probability formula:
P(X = x) = [tex]^nC_x p^x(1-p)^{n-x}[/tex]
The required probability :
P(x=0)
[tex]=\ ^4C_0(0.11)^0(1-0.11)^4\\\\=(1)(1)(0.89)^4\\\\=0.62742241\\\\\approx0.6274[/tex]
Hence, the probability that none of the 4 people get an injection-site reaction would be 0.6274.
Learn more about binomial distribution here:
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