Homework SourseAt times the weight of a product is an important variable to
At times, the weight of a product is an important variable tocontrol. Specifications are given for the weight of a certainpackaged product and a package is rejected if it is either toolight or too heavy. Historical data suggest that 0.95 is theprobability that the product meets weight specifications whereas0.002 is the probability that the product is too light. For eachsingle packaged product the manufacturer invests $20.00 inproduction and the purchase price by the consumer is $ 25.00.
a) What is the probability that a package chosen randomly fromthe production line it too heavy?
b) For each 10,000 packages sold, what profit is received bythe manufacturer if all packages meet weight specification?
c) Assuming that all \"defective\" packages are rejected andrendered worthless, how much is the profit reduced on 10,000packages due to failure to meet weight specification?
At times, the weight of a product is an important variable tocontrol. Specifications are given for the weight of a certainpackaged product and a package is rejected if it is either toolight or too heavy. Historical data suggest that 0.95 is theprobability that the product meets weight specifications whereas0.002 is the probability that the product is too light. For eachsingle packaged product the manufacturer invests $20.00 inproduction and the purchase price by the consumer is $ 25.00.
a) What is the probability that a package chosen randomly fromthe production line it too heavy?
b) For each 10,000 packages sold, what profit is received bythe manufacturer if all packages meet weight specification?
c) Assuming that all \"defective\" packages are rejected andrendered worthless, how much is the profit reduced on 10,000packages due to failure to meet weight specification?
Solution
data suggest that 0.95 is the probability that the productmeets weight specifications , P(W) =0.95
.002 is the probability that the product is too light,P(L)=0.002
a) the probability that the product is too heavy P(H) =1-0.95-0.002 = 0.048
b) For each 10,000 packages sold, what profit is received bythe manufacturer if all packages meet weight specification?
Its given that For each single packaged product themanufacturer invests $20.00 in production and the purchase price bythe consumer is $ 25.00.Hence profit = $(25 - 20) =$5
hence For each 10,000 packages sold, profit receivedby the manufacturer if all packages meet weight specification=
10000 x 5 = $ 50000
c) Assuming that all \"defective\" packages are rejected andrendered worthless, how much is the profit reduced on 10,000packages due to failure to meet weight specification
probability of packages that fail to meet weightspecification = 0.05
hence, no. of defectives in 10000 packages = 10000 x 0.05 =500
profit which could have been earned if these were notdefective = 500 x 5 = $2500
hence $2500 profit reduced on 10,000 packages dueto failure to meet weight specification
b) For each 10,000 packages sold, what profit is received bythe manufacturer if all packages meet weight specification?
Its given that For each single packaged product themanufacturer invests $20.00 in production and the purchase price bythe consumer is $ 25.00.Hence profit = $(25 - 20) =$5
hence For each 10,000 packages sold, profit receivedby the manufacturer if all packages meet weight specification=
10000 x 5 = $ 50000
c) Assuming that all \"defective\" packages are rejected andrendered worthless, how much is the profit reduced on 10,000packages due to failure to meet weight specification
probability of packages that fail to meet weightspecification = 0.05
hence, no. of defectives in 10000 packages = 10000 x 0.05 =500
profit which could have been earned if these were notdefective = 500 x 5 = $2500
hence $2500 profit reduced on 10,000 packages dueto failure to meet weight specification
c) Assuming that all \"defective\" packages are rejected andrendered worthless, how much is the profit reduced on 10,000packages due to failure to meet weight specification
probability of packages that fail to meet weightspecification = 0.05
hence, no. of defectives in 10000 packages = 10000 x 0.05 =500
profit which could have been earned if these were notdefective = 500 x 5 = $2500
hence $2500 profit reduced on 10,000 packages dueto failure to meet weight specification
