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Sagot :
The probability that exactly 5 out of the first 10 customers buy a magazine is 0.00126.
Given suspicion of 9.7% that buy a magazine is correct.
We have to find the probability that exactly 5 out of the first 10 customers buy a magazine. Probability is the chance of happening an event among all the events possible.
The binomial distribution is the probability of exactly x successes on n repeated trials and X can only have two outcomes.
[tex]P(X=x)=C_{n,x}p^{x} (1-p)^{n-x}[/tex]
In which [tex]C_{n,x}=n!/x!(n-x)![/tex]
And P is the probability of happening of X.
In the question 9.7% of his customers buy a magazine.
So the value of P=0.097
This can be calculated by :
P(X=5) when n=13
[tex]P(X=x)=C_{n,x} p^{x} (1-p)^{n-x}[/tex]
[tex]P(X=5)=C_{10,5} (0.097)^{5} (1-0.097)^{10-5}[/tex]
=[tex]P(X=5)=C_{10,5} (0.097)^{5} (0.903)^{5}[/tex]
[tex]=10!/5!5!*0.0000085*0.600397[/tex]
=252*0.00000510
=0.001286
Hence the probability that exactly 5 out of the first 10 customers buy a magazine is 0.001286.
Learn more about probability at https://brainly.com/question/24756209
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