Question

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 5.37215 g and a standard deviation of .05421 g. Identify the weights that are significantly low or significantly high.


What weights are significantly​ low? ​(Round to five decimal places as needed. Use ascending​ order.)

What weights are significantly​ high?

​(Round to five decimal places as needed. Use ascending​ order.)

Answer 1

z₁ = 5,361308 this value, and values below this value, should be considered significantly low

z₂ = 5,48057 this value, and values above this value, should be considered significantly high

Explanation:

z (score) = z₁ - μ₀ / σ

where μ₀ is mean and σ the standard deviation.

if z (score) is equal to -2 ( or less) then

-2 = (z₁ - 5,37215)/0,05421

( -2 )*0,05421 = z₁ - 5,37215

- 0,10842 = z₁ - 5,37215

z₁ = 5,37215 - 0,010842

z₁ = 5,361308

And if z = 2

2* 0,05421 = z₂ - 5,37215

0,10842 = z₂ - 5,37215

z₂ = 5,37215 + 0,10842

z₂ = 5,48057