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The Probability Of A Shipment Passing The Test Assignment Paper A supplier regularly ships spare bulbs in bulk to the theater and promises a 95% reliability (lasting at least 100 hours). The theater inspects each incoming shipment of bulbs by lighting 20 bulbs for 100 hours. If two or more bulbs go out during the test, the batch shipment is returned to the supplier. If the bulbs indeed have a 95% reliability, what is the likelihood that a shipment passes the test? Please includes EXCEL function formulas ORDER YOUR PAPER NOW Step-by-step Step 1/1 The probability of a shipment passing the test can be calculated using the binomial distribution formula, which is: P(X = k) = C(n, k) * p^k * (1 - p)^(n - k) Where: P(X = k) is the probability of getting k successes (in this case, bulbs that last at least 100 hours) in n trials (20 bulbs). C(n, k) is the number of ways to choose k items from a set of n items (also known as the binomial coefficient). p is the probability of success in each trial (0.95, as the supplier promises a 95% reliability). (1 - p) is the probability of failure in each trial (0.05)The Probability Of A Shipment Passing The Test Assignment Paper. To calculate the probability of passing the test, we need to find the probability of having less than two failures in a sample of 20 bulbs, which is: P(X < 2) = P(X = 0) + P(X = 1) P(X = 0) = C(20, 0) * 0.95^0 * 0.05^20 = 0.000000958 P(X = 1) = C(20, 1) * 0.95^1 * 0.05^19 = 0.000024648 P(X < 2) = 0.000000958 + 0.000024648 = 0.000025606 Therefore, the probability of passing the test is 0.000025606 or 0.00256%. We can also use the Excel function BINOM.DIST to calculate the probability. The formula would be: =BINOM.DIST(1,20,0.95,TRUE)+BINOM.DIST(0,20,0.95,TRUE) Where: The Probability Of A Shipment Passing The Test Assignment Paper 1 represents the number of failures that would cause the batch to fail (i.e., 2 or more bulbs going out). 20 is the number of trials (i.e., the number of bulbs tested). 0.95 is the probability of success in each trial (i.e., the 95% reliability promised by the supplier). TRUE indicates that the function should return the cumulative distribution function (i.e., the probability of having 1 or fewer failures). This formula returns a value of 0.000025606, which confirms our earlier result. Final answer Therefore, the probability of passing the test is 0.000025606 or 0.00256% The Probability Of A Shipment Passing The Test Assignment Paper
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Expert Answer

The Probability Of A Shipment Passing The Test Assignment Paper A supplier regularly ships spare bulbs in bulk to the theater and promises a 95% reliability (lasting at least 100 hours). The theater inspects each incoming shipment of bulbs by lighting 20 bulbs for 100 hours. If two or more bulbs go out during the test, the batch shipment is returned to the supplier. If the bulbs indeed have a 95% reliability, what is the likelihood that a shipment passes the test? Please includes EXCEL function formulas

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Step-by-step

Step 1/1
The probability of a shipment passing the test can be calculated using the binomial distribution formula, which is:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
  • P(X = k) is the probability of getting k successes (in this case, bulbs that last at least 100 hours) in n trials (20 bulbs).
  • C(n, k) is the number of ways to choose k items from a set of n items (also known as the binomial coefficient).
  • p is the probability of success in each trial (0.95, as the supplier promises a 95% reliability).
  • (1 - p) is the probability of failure in each trial (0.05)The Probability Of A Shipment Passing The Test Assignment Paper.
To calculate the probability of passing the test, we need to find the probability of having less than two failures in a sample of 20 bulbs, which is:
P(X < 2) = P(X = 0) + P(X = 1)
P(X = 0) = C(20, 0) * 0.95^0 * 0.05^20 = 0.000000958 P(X = 1) = C(20, 1) * 0.95^1 * 0.05^19 = 0.000024648
P(X < 2) = 0.000000958 + 0.000024648 = 0.000025606
Therefore, the probability of passing the test is 0.000025606 or 0.00256%.
We can also use the Excel function BINOM.DIST to calculate the probability. The formula would be:
=BINOM.DIST(1,20,0.95,TRUE)+BINOM.DIST(0,20,0.95,TRUE)
Where: The Probability Of A Shipment Passing The Test Assignment Paper
  • 1 represents the number of failures that would cause the batch to fail (i.e., 2 or more bulbs going out).
  • 20 is the number of trials (i.e., the number of bulbs tested).
  • 0.95 is the probability of success in each trial (i.e., the 95% reliability promised by the supplier).
  • TRUE indicates that the function should return the cumulative distribution function (i.e., the probability of having 1 or fewer failures).
This formula returns a value of 0.000025606, which confirms our earlier result.
Final answer
Therefore, the probability of passing the test is 0.000025606 or 0.00256%
The Probability Of A Shipment Passing The Test Assignment Paper

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