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

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:

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:

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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