Question

If a certain machine makes electrical resistors having a mean resistance of 40 ohms and a standard deviation of 2 ohms, what is the probability that a random sample of 36 of these resistors will have a combined resistance of more than 1458 ohms?

Answer 1

Answer:0.0668

Step-by-step explanation:

Given

mean of sample $\mu =40$

Standard deviation $\sigma =2$

For $n=36$ sample

Random variable $Z=\frac{X-\mu }{\frac{\sigma }{\sqrt{n}}}$

For combined resistance of 1458 ohm mean resistance of $\mu =\frac{1458}{36}=40.5$

$P(40.5$

$=P(\frac{40.5-40}{\frac{1}{3}}$

$=P(1.5$

$=1-P(Z\leq 1.5)$

$=1-0.9332$

$=0.0668$