Question

A data set lists weights (grams) of a type of coin. those weights have a mean of g and a standard deviation of g. identify the weights that are significantly low or significantly high.

Answer 1

The weights that are significantly low z₁ = 5.361308 grams and significantly high z₂ = 5.48057 grams  

What is Z -score?

A Z-score is defined as the fractional representation of data point to the mean using standard deviations.

z -score = (z₁ - μ₀) / σ

where μ₀  is the mean and σ the standard deviation.

Consider a value to be significantly low if its z score is 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.

Here μ₀ = 5,37215 and σ = 0.05421

Substitute z -score = -2

⇒ -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

Here μ₀ = 5,37215 and σ = 0.05421

Substitute z -score = 2

⇒ 2(0.05421) = z₂ -  5.37215

⇒ 0.10842 = z₂ - 5.37215

⇒z₂ = 5.37215 + 0.10842

⇒ z₂ = 5.48057  

Therefore, the weights that are significantly low z₁ = 5.361308 grams and significantly high z₂ = 5.48057 grams

Learn more about the z-score here:

brainly.com/question/13793746

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Your question is incomplete, probably the complete question is:

A data set lists the 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.

Consider a value to be significantly low if its z score is 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.