Question

The resistance of a strain gauge is normally distributed with a mean of 100 ohms and a standard deviation of 0.3 ohms. To meet the specification, the resistance must be within the range 100±0.7 ohms. What proportion of gauges is acceptable? Round your answer to four decimal places.

Answer 1

Answer: 0.6827

Step-by-step explanation:

Given : The resistance of a strain gauge is normally distributed .

Population mean : $\mu=100$

Standard deviation : $\sigma=0.3$

Let x be the random variable that represents the resistance of a strain gauge is normally distributed .

z-score : $z=\dfrac{x-\mu}{\sigma}$

To meet the specification, the resistance must be within the range 100±0.7 ohms i.e. (99.3,100.7).

For x = 100.7

$z=\dfrac{100.7-100}{0.7}=1$

For x = 99.3

$z=\dfrac{99.3-100}{0.7}=-1$

By using the standard normal distribution table, The proportion of gauges is acceptable is given by:-

$P(99.3$

Hence, the proportion of gauges is acceptable=0.6827