Question

Consider a value to be significantly low if its z score less than or equal to 

minus -2 or consider a value to be significantly high if its z score is greater than or equal to 2. A data set lists weights​ (grams) of a type of coin. Those weights have a mean of 

5.37494 g and a standard deviation of 0.05202 g. Identify the weights that are significantly low or significantly high.

Answer 1

$$Z=\dfrac{X-\mu}{\sigma}=>X=Z\sigma+\mu$$

Given $\mu=5.37494 \ g, \sigma=0.05202 \ g$

$$Z=-2, X=-2(0.05202)+5.37494=5.2709(g)$$ $$Z=2, X=2(0.05202)+5.37494=5.47898(g)$$

The weights no more than 5.2709 g are  significantly low.

The weights no less than 5.47898 g are  significantly high.