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
The first thing you have to do is find the z score. z=(20.75-22)/.5 The z would be -2.5 Then, to find the probability, you can use your graphing calculator. Hit 2nd, then catalog, then go down to normalpdf. When that comes up, plug in -2.5 and it should give you a probability of .0175.
Hope that helps!
If you don't have a graphing calculator, you can find table in the back of your statistics text labeled something like "areas under normal distribution" to find the probability.
I hope that helps a little more.
To find the probability that a loaf of bread is less than 20.75 ounces, we need to use the concept of the normal distribution and Z-scores.
Step 1: Convert the value 20.75 ounces to a Z-score.
The Z-score represents the number of standard deviations a given value is from the mean in a normal distribution. Mathematically, the Z-score is calculated using the formula:
Z = (X - μ) / σ
Where:
X = the given value (20.75 ounces)
μ = the mean of the distribution (22 ounces)
σ = the standard deviation of the distribution (0.5 ounces)
Substituting the values into the formula:
Z = (20.75 - 22) / 0.5
Z ≈ -2.5
Step 2: Find the probability corresponding to the Z-score.
Now, we need to find the probability corresponding to the Z-score of -2.5. We can use a standard normal distribution table or a calculator with a normal distribution function.
Using a standard normal distribution table, we can look up the Z-score of -2.5 and find the corresponding probability. The table will show a value close to 0.0062.
So, the probability that a loaf of bread is less than 20.75 ounces is approximately 0.0062 or 0.62%.