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 5.13125 g and a standard deviation of 0.05783 g. Identify the weights that are significantly low or significantly high.

Answer 1

SOLUTION:

From given data,

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 5.13125 g and a standard deviation of 0.05783 g. Identify the weights that are significantly low or significantly high.

We have,

mean = = 5.13125

standard deviation = = 0.05783

z - score = (x - ) /

( x - 5.13125) / 0.05783 <= -2

( x - 5.13125) <= -0.11566

x <= -0.11566+5.13125

X <= 5.01559

Therefore the significant low score is 5.01559

z - score = (x - ) /

( x - 5.13125) / 0.05783 >= 2

( x - 5.13125) >= 0.11566

x >=0.11566+5.13125

X <= 5.24691

Therefore the significant high score is 5.24691