Find the indicated probability or percentage for the normally distributed variable.
-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)2.28%
C)47.72%
D)37.45%

Question

Find the indicated probability or percentage for the normally distributed variable.
-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)2.28%
C)47.72%
D)37.45%

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 $X$ is the value in question, $\mu$ is the mean, and $\sigma$ is the standard deviation. Substituting the given values, we get $z = \frac{(0.32 - 0.30)}{0.01} = 2$. Looking up the z-score of 2 in a standard normal distribution table or using a calculator, we find that the area to the left of z=2 is approximately 0.9772, which means 97.72% of the bolts have a diameter less than 0.32 inches. Therefore, the percentage of bolts with a diameter greater than 0.32 inches is 100% - 97.72% = 2.28%.

Find the Indicated Probability or Percentage for the Normally Distributed