# 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
Measurement 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. 2021-02-15
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:
$$z=\frac{y-E(y)}{S.D(y)}=\frac{y-\mu}{s}-N(0.1)$$
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:
$$P(y>13)=1-P(y\leq 13)$$
$$=1-P((y-\frac{10}{2})\leq \frac{13-10}{2})$$
$$=1-P((y-E\frac{y}{S}.D(y))\leq (1.5)$$
$$=1-P(Z\leq 1.5)$$
$$\cong1-\phi(1.5),\left[Fromcthe\ table\ values\ of\ standard\ normal\ distribution.\ The\ area\ corresponding\ to\ left\ of\ 1.5\ is\ 0.06681\right]$$
$$\cong1-0.93319\cong0.06681$$
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 milliamperes. That is, $$9 < y < 11$$.
The value of $$P(9 < y < 11)$$ is obtained as 0.38292 from the calculation given below:
$$P(9 \(=P(-0.5<(y-E\frac{y}{S.D(y)}<(0.5)$$</span>
$$=P(-0.5 \(=\phi(0.5)-\phi(-0.5)$$
$$\cong2\phi(0.5)-1$$
$$\cong(2\times 0.69146)-1,\left[From\ the\ table\ values\ of\ standard\ normal\ distribution.\ The\ area\ corresponding\ to\ left\ of\ 0.5\ is\ 0.69146\right]$$
$$\cong0.38292$$
Step 4
The probability that the current measurement exceeds 13 milliamperes is 0.06681.
The probability that the current measurement lies between 9 and 11 milliamperes is 0.38292.

### Relevant Questions Loretta, who turns eighty this year, has just learned about blood pressure problems in the elderly and is interested in how her blood pressure compares to those of her peers. Specifically, she is interested in her systolic blood pressure, which can be problematic among the elderly. She has uncovered an article in a scientific journal that reports that the mean systolic blood pressure measurement for women over seventy-five is 133.0 mmHg, with a standard deviation of 5.1 mmHg.
Assume that the article reported correct information. Complete the following statements about the distribution of systolic blood pressure measurements for women over seventy-five.
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(a) What is the standard deviation of Juan's mean result? (That is, if Juan kept making sets of 3 measurements and averaging them, what would be the standard deviation of all his xbar's?)
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What is the standard deviation of this estimate ? True or False
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4.The median is the most commonly used measure of central tendency.
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8.In a distribution with a mean of M = 76 and a standard deviation of SD = 7, a score of 91 would be considered an extreme value.
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