A hardware store chain purchases large shipments of lightbulbs from the manufacturer described above and specifies that each shipment must contain no more than 7% defectives. When the manufacturing process is in control, what is the probability that the hardware store's specifications are met? (Round your answer to four decimal places.)

Question

Mathematics

Lizbeth Jenkins

26 December, 05:55

A hardware store chain purchases large shipments of lightbulbs from the manufacturer described above and specifies that each shipment must contain no more than 7% defectives. When the manufacturing process is in control, what is the probability that the hardware store's specifications are met? (Round your answer to four decimal places.)

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Kiley · Answer 1

Question:

The question is incomplete. Find below the complete question and the answer.

The table lists the number of defective 60-watt lightbulbs found in samples of 100 bulbs selected over 25 days from a manufacturing process. Assume that during this time the manufacturing process was not producing an excessively large fraction of defectives. Day 1 2 3 4 5 6 7 8 9 10 Defectives 4 2 5 9 4 4 5 5 6 2 Day 11 12 13 14 15 16 17 18 19 20 Defectives 2 5 4 4 0 3 4 1 4 0 Day 21 22 23 24 25 Defectives 3 3 4 5 3 A hardware store chain purchases large shipments of lightbulbs from the manufacturer described above and specifies that each shipment must contain no more than 7% defectives. When the manufacturing process is in control, what is the probability that the hardware store's specifications are met? (Round your answer to four decimal places.)

Answer:

The probability = 0.9633

Step-by-step explanation:

Given Data;

Day 1 2 3 4 5 6 7 8 9 10

Defectives 4 2 5 9 4 4 5 5 6 2

Day 11 12 13 14 15 16 17 18 19 20

Defectives 2 5 4 4 0 3 4 1 4 0

Day 21 22 23 24 25

Defectives 3 3 4 5 3

N = 100 bulbs

calculating the mean of the sample, we have

Sample mean (xbar) = sum of the number of defectives/number of days

(4 + 2+5 + 9 + 4 + 4 + 5 + 5 + 6 + 2 + 2 + 5 + 4 + 4 + 0 + 3 + 4+

1 + 4 + 0 + 3 + 3 + 4 + 5 + 3) / 25

= 91/25

= 3.64

Sample proportion (p) = 3.64 / 100

= 0.0364

We need to find the Probability of P (p < 0.07)

From the formula of Z score:

Z = (P^ - P) / sqrt (P * (1-P) / n)

Substituting, we have,

Z = (0.07 - 0.0364) / √ (0.0364 * (1-0.0364) / 100)

= 0.0336/√0.00035075

=0.0336 / 0.0187

Z = 1.79

P (z < 1.79) can be obtained from the Z table as 0.9633

The probability that the hardware store's specifications are met is