Answer:
25.25%
Explanation:
Mean diameter (μ) = 0.35 inches
Standard deviation (σ) = 0.03 inches
For any given diameter, X, the z-score is given by:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
For X= 0.37 inches:
[tex]z=\frac{0.37-0.35}{0.03}\\z=0.6667[/tex]
A z-score of 0.6667 is equivalent to the 74.75-th percentile of a normal distribution.
Therefore, the percentage of bolts that will have a diameter greater than 0.37 inches is:
[tex]P(X>0.37) = 100 - 74.75\\P(X>0.37) = 25.25\%[/tex]
