Answer:
Her z-score is 2.03.
Step-by-step explanation:
In a set with mean and standard deviation
, the zscore of a measure X is given by:
Michelle’s height is 1.758 meters. What is her z-score?
Michelle's is a woman.
The average height of women is and the standard deviation is
This is Z when X = 1.758. So
Her z-score is 2.03.
Answer:
19 nails
Step-by-step explanation:
Let's first determine the z-score by using the formula:
Where x=5.03, μ=5, σ=0.03 and so:
We can now use a z-score table to determine that 1.00 is synonymous with 0.8413 meaning 84.13%. This means that 84.13% of the nails are less than or equal to 5.03 inches long. Therefore, since we know 100% = 1 in decimals we can determine that the length greater than 5.03 inches is 1-0.8413=0.1587. This means that 15.87% of the 120 nails are greater than 5.03 inches long.
Finally, we can determine how many nails are greater than 5.03 by determining what is 15.87% of 120 which is:
And so 19 out of the 120 nails are greater than 5.03 inches long.