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

Immanuel Peters

4 December, 02:18

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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Savanna Liu · 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