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Reika [66]
2 years ago
13

If a set of sample measurements has a mean of 100, a normal distribution, a standard deviation of 2, and control limits of 94 an

d 106, what percentage of the samples are expected to be between 94 and 106? Explain your answer.
Mathematics
1 answer:
weeeeeb [17]2 years ago
6 0

Answer: 99.73%

Step-by-step explanation:

Given : Mean : \mu=100

Standard deviation : \sigma=2

Let X be the random variable that represents the data values.

Formula for Z-score :  z=\dfrac{X-\mu}{\sigma}

For x=94, we have

z=\dfrac{94-100}{2}=-3

For x=106, we have

z=\dfrac{106-100}{2}=3

The probability that the samples are between 94 and 106:-

P(-3

Hence, the percent of the samples are expected to be between 94 and 106 = 99.73%

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