Answer:
0.8937
Step-by-step explanation:
This is a case of binomial probability with n = 64, p = 0.10 and x = 3. This means that the probability of a cancellation is 10%. Here, we can find the probability that more than 3 cancellations or no shows will occur by finding binompdf(64,0.10, 0) + binompdf(64,0.10, 1) + binompdf(64,0.10, 2) + binompdf(64,0.10, 3) and then subtracting this sum from 1.000.
We get: 0.0012 + 0.0084 + 0.0293 + 0.0674 = sum = 0.1063
Then the desired probability is 1.0000 - 0.1063 = 0.8937
The probability that more than 3 cancellations and/or no-shows will occur during the next week is: 0.8937
This involves binomial probability distribution with the formula;
P(X = x) = ⁿCₓ × pˣ × q⁽ⁿ ⁻ ˣ⁾
We are given;
p = 10% = 0.1
n = 64
q = 1 - p = 1 - 0.1
q = 0.9
We want to find the probability that more than 3 cancellations and/or no-shows will occur during the next week is given by;
P(X > 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X =3))
From online binomial probability calculator;
P(0) = 0.0012
P(1) = 0.0084
P(2) = 0.0293
P(3) = 0.0674
Thus;
P(X > 3) = 1 - (0.0012 + 0.0084 + 0.0293 + 0.0674 )
P(X > 3) = 1 - 0.1063
P(X > 3) = 0.8937
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