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:

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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.)

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

16.9 times 2.85

step-by-step explanation: