Question #333777

On average, four students visits the Mathematics and Statistics tutoring centre during a 5-minute period.

(a) Calculate the probability that three students visit the centre during a 5 minute period. (3)

(b) During a ten-minute period, what is the probability that at least 4 students visit the centre? (5)


1
Expert's answer
2022-04-27T00:44:18-0400

Let XX be the random variable, X=X = number of students visiting the centre during t-minute period

XPo(λt)X\sim Po(\lambda t)

(a)

λt=4\lambda t=4


P(X=3)=e4(4)33!=0.195367P(X=3)=\dfrac{e^{-4}\cdot(4)^3}{3!}=0.195367

(b)

λt=8\lambda t=8


P(X4)=1P(X<4)P(X\ge4)=1-P(X<4)

=1e8(8)00!e8(8)11!=1-\dfrac{e^{-8}\cdot(8)^0}{0!}-\dfrac{e^{-8}\cdot(8)^1}{1!}

e8(8)22!e8(8)33!-\dfrac{e^{-8}\cdot(8)^2}{2!}-\dfrac{e^{-8}\cdot(8)^3}{3!}

=0.957620=0.957620


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