UPS currently believes that it achieves a 96 % on-time performance for its customers. A random sample of 200 customer shipment studies has shown that 188 of them have met the on-time delivery promise. What is the probability that a random sample of 200 customer shipments would contain 188 or fewer on-time deliveries if the true population of on-time deliveries is 96%? Would you be surprised if the random sample of 200 customer shipments had 197 on-times deliveries? Support your answer with a probability calculation. Suppose the random sample of 200 customer shipments revealed that 178 were on time. Would such a finding cause you to question UPS’s claim that its on-time performance is 96%? Support your answer with a probability calculation.
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UPS currently believes that it achieves a 96 % on-time performance for its customers. A random sample of 200 customer shipment studies has shown that 188 of them have met the on-time delivery promise.
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What is the
probability that a random sample of 200 customer shipments would contain 188 or fewer on-time deliveries if the true population of on-time deliveries is 96%? -
Would you be surprised if the random sample of 200 customer shipments had 197 on-times deliveries? Support your answer with a probability calculation.
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Suppose the random sample of 200 customer shipments revealed that 178 were on time. Would such a finding cause you to question UPS’s claim that its on-time performance is 96%? Support your answer with a probability calculation.
Given information:
p = 0.96
n = 200
1)
x = 188
By applying binomial distribution:-
Use the excel formula, "=BINOM.DIST(188,200,0.96,TRUE)" for determining the probability:
The probability that a random sample of 200 customer shipments would contain 188 or fewer on-time deliveries if the true population of on-time deliveries is 96% is 0.1075.
2)
x = 197
By applying binomial distribution:-
Use the excel formula, "=BINOM.DIST(197,200,0.96,False)" for determining the probability:
We would be surprised if the random sample of 200 customer shipments had 197 on-times deliveries, because the obtained probability(0.0270) is less than 0.05.
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