Question 1086635: The United Package Service has a policy that states if a package is delivered late they will reimburse their shipping fees. They deliver packages late only 5% of the time. If a delivery person has 7 deliveries one day, what is the probability that at most 1 package is arriving late? Round your answer to the nearest ten-thousandth.
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website! Question:
The United Package Service has a policy that states if a package is delivered late they will reimburse their shipping fees. They deliver packages late only 5% of the time. If a delivery person has 7 deliveries one day, what is the probability that at most 1 package is arriving late? Round your answer to the nearest ten-thousandth.
Solution:
To determine if the problem can be modelled using the binomial distribution, we need to examine the following criteria:
1. Bernoulli trials, i.e. exactly two possible outcomes (Late or not late)
2. Number of trials is known before experiment, i.e. independent of outcomes (7 per day)
3. All trials are independent of each other (assumed true)
4. Probability of success is known, and remain constant throughout trials (p=5%=0.05)
Since all the criteria are satisfied, binomial distribution will be used.
The probability of x successes out of N trials each with probability of success p is given by
P(x)=C(N,x)(p^x)(1-p)^(N-x)
where
C(N,x) is number of combinations of selecting x objects out of N.
p=0.05
n=7
x=0 and x=1
P("at most one package late") =P(0)+P(1)
=C(7,0)*0.05^0*(1-0.05)^7+C(7,1)*0.05^1*(1-0.05)^6
=0.6983+0.2573
=0.9556
Probability of at most one delivery late is 0.9556.
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