A loaf of bread is normally distributed with a mean of 22 ounces and a standard deviation of .5 ounces. What is the probability that a loaf of bread is < 20.75 ounces?
Z = (x - μ)/SD
Z = (20.75 - 22)/.5
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion less than that Z score.
To find the probability that a loaf of bread is less than 20.75 ounces, we can use the concept of standard normal distribution.
1. Convert the given values to standard units:
- Calculate the z-score for 20.75 ounces:
z = (x - μ) / σ
where x = 20.75 ounces, μ = mean = 22 ounces, σ = standard deviation = 0.5 ounces
z = (20.75 - 22) / 0.5
2. Calculate the probability using a standard normal distribution table or calculator:
- Look up the z-score in the standard normal distribution table or use a calculator to find the corresponding cumulative probability.
For example, if you use a table and find that the z-score of 20.75 is approximately -2.5, you can find the probability by looking up the corresponding value in the table. The table will give you the probability associated with a z-score of -2.5, which represents the area under the standard normal curve to the left of -2.5.
3. Interpret the probability:
- The probability you obtain represents the likelihood that a loaf of bread is less than 20.75 ounces.