Answer to Question #143908 in Statistics and Probability for Vladimyr Lubin

Question

(3.3.11) Consider a value to be significantly low if its z score less than or equal to -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 5.28353 g and a standard deviation of 0.06149 g. Identify the weights that are significantly low or significantly high.
What weights are significantly​ low?
A.Weights that are less than

B.Weights that are between and
.
C.Weights that are greater than

Answer 1

$$Z=\frac{x-\mu}{\sigma}$$

$\mu=5.28353$ and $\sigma=0.06149$

Weights are significantly low if its z score less than or equal to -2, hence

$Z=-2 \implies \frac{x-5.28353}{0.06149}=-2 \implies x=5.16055$

Weights are significantly high if its z score greater than or equal to 2, hence

$Z=2 \implies \frac{x-5.28353}{0.06149}=2 \implies x=5.40651$

Therefore weights less that 5.16055 are significantly low and weights greater than 5.40651 are significantly high.