Solve the problem.
-The diameters of bolts produced by a certain machine are normally distributed with a mean of $0.30$ inches and a standard deviation of $0.01$ inches. What percentage of bolts will have a diameter greater than $0.32$ inches?
A) $97.72 \%$
B) $47.72 \%$
C) $2.28 \%$
D) $37.45 \%$

Question

Quizplus · Accepted Answer

To find the percentage of bolts with a diameter greater than 0.32 inches, we calculate the z-score for 0.32 inches using the formula $z = \frac{(X - \mu)}{\sigma}$, where $X = 0.32$, $\mu = 0.30$, and $\sigma = 0.01$. This gives us $z = \frac{(0.32 - 0.30)}{0.01} = 2$. Looking up a z-score of 2 in the standard normal distribution table, we find that the area to the left of z=2 is 0.9772, meaning 97.72% of the distribution is below 0.32 inches. Therefore, the percentage above 0.32 inches is 100% - 97.72% = 2.28%.

Solve the Problem 0.300.300.30 Inches and a Standard Deviation Of 0.010.010.01 Inches What Percentage of Bolts Will Have a Diameter Greater

Solve the Problem $0.30$ Inches and a Standard Deviation Of $0.01$ Inches What Percentage of Bolts Will Have a Diameter Greater