Question

A data set lists the weights​ (grams) of a type of coin. Those weights have a mean of 5.41478 g and a standard deviation of 0.06439 g. Identify the weights that are significantly low or significantly high.

Answer 1

QUESTION

Consider a value to be significantly low if its z score is less than or equal to -2 or consider the value to be significantly high if its z score is greater than or equal to 2. A data set lists the weights​ (grams) of a type of coin. Those weights have a mean of 5.41478 g and a standard deviation of 0.06439 g. Identify the weights that are significantly low or significantly high.

SOLUION

Given, mean, $\mu=5.41478$ and standard deviation, $\sigma=0.06439$

The formula to z-score, $Z=\frac{x-\mu}{\sigma}$

But the values of $Z$ are given. So, $x=\mu+Z\sigma$

We are going to calculate $x$ when $Z$ is at $-2$ and $2$

When $Z$ is at $-2$,

Then $x=5.41478-2(0.06439)$

$x=5.286$

When $Z$ is at $2$

Then $x=5.41478+2(0.06439)$

$x=5.54356$

ANSWER: The weight that are significantly low $=5.286$ and the weight that is significantly high $=5.54356$