Find the indicated probability or percentage for the normally distributed variable.
-Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standard deviation 0.070 g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g.
What percentage of legal quarters will be rejected?
A)1.62%
B)2.48%
C)0.0196%
D)1.96%

Question

Find the indicated probability or percentage for the normally distributed variable.
-Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standard deviation 0.070 g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g.
What percentage of legal quarters will be rejected? 
A)1.62%
B)2.48%
C)0.0196%
D)1.96%

Quizplus · Accepted Answer

To find the percentage of quarters rejected, calculate the probability that a quarter's weight is less than 5.48 g or more than 5.82 g. Using the standard normal distribution, find the z-scores for 5.48 g and 5.82 g, then find the cumulative probabilities. Subtract the cumulative probability between these z-scores from 1 to get the rejection percentage, which is approximately 1.96%.

Find the Indicated Probability or Percentage for the Normally Distributed