At a doctor's office, patients arrive at a rate of ten per hour. With

Baublysiz

Baublysiz

Answered question

2021-11-17

At a doctor's office, patients arrive at a rate of ten per hour. With a probability of 12, each is either young or old. Assume you know that exactly ten young people arrived within an hour (say, 10 to 11am)
a) Compute the probability that exactly 10 old patients also entered.
b) Compute the probability that at least 20 patients have entered

Answer & Explanation

Momp1989

Momp1989

Beginner2021-11-18Added 21 answers

Step 1
Given information:
Given that at a doctor’s office, patients arrive at a rate of 10 per hour with a probability of 0.5.
Step 2
a) Compute the probability that exactly 10 old patients also entered:
The probability that exactly 10 old patients also entered is obtained as given below:
X= Number of old patients
XP(λ=0.5×10=5)
P(X=10)=e5×51010!
=65800.263663628800
=0.0181
Thus, the probability that exactly 10 old patients also entered is 0.0181.
Step 3
b) Compute the probability that at least 20 patients have entered:
The probability that at least 20 patients have entered is obtained as given below:
P(X20)=1P(X19)
=1x=019e10×10xx!
=10.9965
=0.0035
Thus, the probability that at least 20 patients have entered is 0.0035.

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