Suppose that the current measurements in a strip of wire are assumed to follow a normal distribution with a mean of 10 milliamperes and a standard deviation of 2 milliamperes. What is the probability that a measurement exceeds 13 milliamperes? What is the probability that a current measurement is between 9 and 11 milliamperes

Question
Asked Feb 25, 2019

Suppose that the current measurements in a strip of wire are assumed to follow a normal distribution with a mean of 10 milliamperes and a standard deviation of 2 milliamperes. What is the probability that a measurement exceeds 13 milliamperes? What is the probability that a current measurement is between 9 and 11 milliamperes

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Expert Answer

Step 1

Standard normal distribution:

The standard normal distribution is a special case of normal distribution. The standard normal distribution will have mean 0 and standard deviation 1. If a random variable y follows normal distribution with mean (m) and standard deviation (s), then the standard normal variable z will be as given below:

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Step 2

Find the probability that the current measurement exceeds 13 milliamperes:

Consider the current measurements in a strip of wire be denoted by y. It is given that the current measurements in a strip of wire are normally distributed.

The mean and standard deviation for current measurements in a strip of wire is y-bar = 10 milliamperes and s(y) = 2 milliamperes, respectively.

The given requirement is that the current measurement in a strip of wire should be greater than 13 milliamperes. That is, y > 13.

The value of P(y > 13) is obtained as 0.06681 from the calculation given below:

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Step 3

Find the probability that the current measurement lies between 9 and 11 milliamperes:

The given requirement is that the current measurement in a strip of wire should lie between 9 and 11 milliampe...

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