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
