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A company uses 85 circuit boards a day in a manufacturing process. The person who orders the boards follows this rule: Order when the amount on hand drops to 625 boards. Orders are delivered approximately six days after being placed. The delivery time is normal with a mean of six days and a standard deviation of 1.10 days. What is the probability that the supply of circuit boards will be exhausted before the order is received if boards are reordered when the amount on hand drops to 625 boards?

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pedrocarratore

Answer:

0.1093 or 10.93%

Explanation:

The number of days before the company runs out of stock after placing an order (X) is:

[tex]X = \frac{Stock}{demand}= \frac{625}{85}\\X= 7.353\ days[/tex]

Assuming a normal distribution with:

Mean (μ) = 6

Standard deviation (σ)=1.10

The z-score for X=7.353 is:

[tex]z=\frac{X- \mu}{\sigma}\\z=\frac{7.353- 6}{1.10}\\z=1.23[/tex]

According to the z-score table, a score of 1.23 falls in the 0.8907-th percentile. Therefore, the probability of the delivery takes longer than 7.353 days is:

[tex]P(X>7.353) = 1 - 0.8907\\P(X>7.353) =  0.1093[/tex]

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