The weights that are significantly low z₁ = 5.361308 grams and significantly high z₂ = 5.48057 grams
<h3>What is Z -score?</h3>
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.
