A loaf of bread is normally distributed with a mean of 22 oz and a standard deviation of 0.5 oz. What is the probability that a loaf is larger than 21 oz?
97.72%
See http://psych.colorado.edu/~mcclella/java/normal/accurateNormal.html
for one of many normal distribution calculating tools online.
To find the probability that a loaf is larger than 21 oz, we need to calculate the area under the normal distribution curve to the right of the value 21.oz
Here's how you can calculate it:
Step 1: Standardize the value 21 oz using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.
z = (21 - 22) / 0.5 = -2
Step 2: Look up the standardized value in the standard normal distribution table (also known as the Z-table) to find the corresponding cumulative probability.
The Z-table provides the probabilities for standard normal distribution values between 0 and a given z-score. However, we are interested in the probability to the right of -2, so we subtract the value in the Z-table from 1.
Using the Z-table, the value corresponding to -2 is 0.0228. So, the probability to the right of -2 is 1 - 0.0228 = 0.9772.
Therefore, the probability that a loaf of bread is larger than 21 oz is approximately 0.9772, or 97.72%.