A manufacturer creates and sells an electronic product that uses one resistor. The product will be defective if its resistor has a resistance below 180 ohms. The manufacturer purchases 1,000 resistors from a new supplier. The supplier claims that the average resistance of their resistors is 200 ohms with a standard deviation of 10 ohms. a. The manufacturer decides to randomly sample n = 4 of the resistors from the batch to check that the average resistance is really 200 ohms. If the estimated average resistance is below 190, the shipment will be sent back. Assuming that the suppliers specifications are correct, what is the probability that the shipment is sent back? (I.e. calculate P(X < 190).) Be sure to state any additional assumptions that you make, if any, to arrive at your answer. b. If the supplier's specification is true and the shipment of resistors is used by the manufacturer, what is the probability that a created product will be defective? State any assumptions needed to arrive at your answer. c. Suppose 980 products end up being created and sold. What is the probability that more than 60 products are returned for being defective? Give an exact probability using the binomial distribution. d. Repeat the calculation in (c), but this time use a normal approximation with a continuity correction. Is the approximation close to the exact value?
A manufacturer creates and sells an electronic product that uses one resistor. The product will be defective if its resistor has a resistance below 180 ohms. The manufacturer purchases 1,000 resistors from a new supplier. The supplier claims that the average resistance of their resistors is 200 ohms with a standard deviation of 10 ohms. a. The manufacturer decides to randomly sample n = 4 of the resistors from the batch to check that the average resistance is really 200 ohms. If the estimated average resistance is below 190, the shipment will be sent back. Assuming that the suppliers specifications are correct, what is the probability that the shipment is sent back? (I.e. calculate P(X < 190).) Be sure to state any additional assumptions that you make, if any, to arrive at your answer. b. If the supplier's specification is true and the shipment of resistors is used by the manufacturer, what is the probability that a created product will be defective? State any assumptions needed to arrive at your answer. c. Suppose 980 products end up being created and sold. What is the probability that more than 60 products are returned for being defective? Give an exact probability using the binomial distribution. d. Repeat the calculation in (c), but this time use a normal approximation with a continuity correction. Is the approximation close to the exact value?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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PLEASE ANSWER PART D ONLY, THE OTHER PARTS ARE NOT REQUIRED.
Thank you.
Transcribed Image Text:A manufacturer creates and sells an electronic product that uses one resistor. The product will be defective if
its resistor has a resistance below 180 ohms. The manufacturer purchases 1,000 resistors from a new supplier.
The supplier claims that the average resistance of their resistors is 200 ohms with a standard deviation of 10
ohms.
a. The manufacturer decides to randomly sample n =
average resistance is really 200 ohms. If the estimated average resistance is below 190, the shipment
will be sent back. Assuming that the suppliers specifications are correct, what is the probability that
the shipment is sent back? (I.e. calculate P(X < 190).) Be sure to state any additional assumptions
that you make, if any, to arrive at your answer.
b. If the supplier's specification is true and the shipment of resistors is used by the manufacturer, what is
the probability that a created product will be defective? State any assumptions needed to arrive at
4 of the resistors from the batch to check that the
your answer.
c. Suppose 980 products end up being created and sold. What is the probability that more than 60
products are returned for being defective? Give an exact probability using the binomial distribution.
d. Repeat the calculation in (c), but this time use a normal approximation with a continuity correction. Is
the approximation close to the exact value?
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