Answer to Question #145244 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? Select the correct answer below and fill in the answer​ box(es) to complete your choice.
A. Weights that are less than?
B. Weights that are between? and?
C. Weights that are greater than?

Answer 1

$\mu=5.28353$

$\sigma = 0.06149$

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

$Z \le -2$ significantly low values:

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

$Z \geq 2$ significantly high values:

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

Answer:

weights less than 5.16055 are significantly​ low,

weights more than 5.40651 are significantly​ high.