You still work at Dockery Manufacturing (still exciting!), and your organization still requires a lead time between 18 and 23 days for supplied items. After further investigating the supplier's process, you determine their current lead times are normally distributed with a process mean of 21 days and a standard deviation of 1.90. What is the percent likelihood that a randomly observed lead time by the supplier would be too short per your firm's specifications? Group of answer choices 5.71% 14.69% 20.58% 35.13% 44.29%

Question

Janiyah Wong

Mathematics

19 May, 17:35

You still work at Dockery Manufacturing (still exciting!), and your organization still requires a lead time between 18 and 23 days for supplied items. After further investigating the supplier's process, you determine their current lead times are normally distributed with a process mean of 21 days and a standard deviation of 1.90. What is the percent likelihood that a randomly observed lead time by the supplier would be too short per your firm's specifications? Group of answer choices 5.71% 14.69% 20.58% 35.13% 44.29%

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Answers (1)

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Daphne Everett · Answer 1

The probability is of 14.69%

Step-by-step explanation:

According to the given data we have the following:

Lead time mean = 21 days

Standard deviation = 1.90

To calculate the percent likelihood that a randomly observed lead time by the supplier would be too short per your firm's specifications we will calculate first the z statisticsas follows:

z = (X - mean) / Standard deviation

z = (23-21) / 1.90

z = 1.05

Then Looking at z table, we will find probability corresponding to z = 1.05. The probability is 0.8531 but the area for z > 1.05 will be 1 - 0.8531 = 0.1469

Therefore, the probability is of 14.69%