Respuesta :
The probability that four or fewer of the people who called will sign up for a class = 0.9805
For given question,
Eric estimates that one out of every five people who call for information about a class will sign up for the class.
Last week he receive nine calls.
We need to find the probability that four or fewer of the people who called will sign up for a class.
Total number of calls = 9
⇒ n = 9
Since one out of every five people who call for information about a class will sign up for the class.
the probability of success (p) = 1/5
= 0.2
and the probability of failure (q) = 1 - p
= 1 - 0.2
= 0.8
To find the probability that four or fewer of the people who called will sign up for a class.
So, x would take values 0, 1, 2, 3, 4
Using Binomial principal,
For x = 0,
[tex]P(x=0)= ~^9C_0(0.2)^0(0.8)^{9-0}\\\\P(x=0)=0.13422[/tex]
For x = 1,
[tex]P(x=1)= ~^9C_1(0.2)^1(0.8)^{9-1}\\\\P(x=1)=0.30199[/tex]
For x = 2,
[tex]P(x=2)= ~^9C_2(0.2)^2(0.8)^{9-2}\\\\P(x=2)=0.30199[/tex]
For x = 3,
[tex]P(x=3)= ~^9C_3(0.2)^3(0.8)^{9-3}\\\\P(x=3)=0.17616[/tex]
For x = 4,
[tex]P(x=4)= ~^9C_4(0.2)^4(0.8)^{9-4}\\\\P(x=4)=0.06606[/tex]
So, the required probability would be,
P = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)
P = 0.1342 + 0.3020 + 0.3020 + 0.1762 + 0.0661
P = 0.9805
Therefore, the probability that four or fewer of the people who called will sign up for a class = 0.9805
Learn more about the probability here:
https://brainly.com/question/3679442
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