Answer:
19 nails
Step-by-step explanation:
Let's first determine the z-score by using the formula:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Where x=5.03, μ=5, σ=0.03 and so:
[tex]z=\frac{5.03-5}{0.03}=1[/tex]
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:
[tex]120 \times 0.1587 \approx 19[/tex]
And so 19 out of the 120 nails are greater than 5.03 inches long.
