The diameter of an electric cable is normally distributed, with a mean of 0.7 inch and a standard deviation of 0.01 inch. What is the probability that the diameter will exceed 0.71 inch?
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
The diameter of an electric cable is normally distributed, with a mean of 0.7 inch and a standard deviation of 0.01 inch. What is the probability that the diameter will exceed 0.71 inch?
To find the probability that the diameter will exceed 0.71 inch, we need to calculate the area under the normal distribution curve to the right of the given value. Here's how you can do it:
Step 1: Standardize the value
First, we need to standardize the given value using the formula:
z = (x - μ) / σ
where:
z = standardized value
x = given value
μ = mean
σ = standard deviation
In this case:
x = 0.71 inch
μ = 0.7 inch
σ = 0.01 inch
Plugging in the values:
z = (0.71 - 0.7) / 0.01
z = 0.01 / 0.01
z = 1
Step 2: Find the area under the normal curve
Next, we need to find the area under the normal distribution curve to the right of the standardized value using a standard normal distribution table or calculator. This area represents the probability.
If you are using a standard normal distribution table:
Look up the z-value of 1 and find the corresponding cumulative probability (also known as the area) in the table. The cumulative probability will give you the probability of the diameter exceeding 0.71 inch.
If you are using a calculator or software:
Use the cumulative distribution function (CDF) with the z-value of 1 to find the probability. The result should represent the probability of the diameter exceeding 0.71 inch.
Remember to check if your table or software gives the probability to the right of the z-value or the left. If it gives the probability to the left, you can subtract it from 1 to get the probability to the right.
Note: Since the normal distribution is symmetrical, the probability of the diameter being less than 0.71 inch would be the same as the probability of it exceeding 0.71 inch.
Once you've determined the method you prefer, follow the steps to find the probability.