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kifflom [539]
3 years ago
5

The diameter of the dot produced by a printer is normally distributed with a mean diameter of 0.002 inch and a standard deviatio

n of 0.0004 inch. What is the probability that a diameter is between 0.0014 and 0.0026 inches
Mathematics
1 answer:
Montano1993 [528]3 years ago
4 0

Answer:

P(0.0014 < x < 0.0026)  = 0.86639

Step-by-step explanation:

Given

\mu = 0.002

\sigma = 0.0004

Required

P(0.0014 < x < 0.0026)

First, calculate the z score

z = \frac{x - \mu}{\sigma}

For x = 0.0014

z = \frac{0.0014 - 0.002}{0.0004}

z = \frac{-0.0006}{0.0004}

z = -1.5

For x = 0.0026

z = \frac{0.0026 - 0.002}{0.0004}

z = \frac{0.0006}{0.0004}

z = 1.5

So, we have:

P(0.0014 < x < 0.0026) = P(-1.5

From z probability table, we have:

P(-1.5

Hence:

P(0.0014 < x < 0.0026)  = 0.86639

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