Diameter of an electric cable is normally distributed with a mean f 0.8 with a standard deviation of 0.01. What is the probability that the diameter will exceed 0.83?
The beauty of the following applet is that you don't even have to convert to z-scores
http://davidmlane.com/hyperstat/z_table.html
Just enter .8 as the mean and .01 as the standard deviation.
Click on "above" and enter .83 to get
.001350
or
you could find the z-scores.
it it easy to see that .83 would be exactly 3 SD's from the mean of 0,
if you enter mean=0, SD = 1, "above" =3 you will get the same result
Or
go to whatever chart you are using, and look up under a score of 3.0, your result should also be .00135
To find the probability that the diameter will exceed 0.83, we can use the standard normal distribution and convert the given values to z-scores.
The z-score is a measure of how many standard deviations an observation or value is from the mean of a normal distribution. It can be calculated using the formula:
z = (x - μ) / σ
where z is the z-score, x is the value we want to convert, μ is the mean, and σ is the standard deviation.
In this case, the mean (μ) is 0.8 and the standard deviation (σ) is 0.01. We want to find the probability of the diameter exceeding 0.83, so x is 0.83.
First, let's calculate the z-score:
z = (0.83 - 0.8) / 0.01
z = 3
Next, we need to find the probability associated with this z-score by referring to the standard normal distribution table or using a statistical calculator. The standard normal distribution table provides the probabilities for different z-scores.
Since we want to find the probability that the diameter exceeds 0.83, we are interested in the area under the curve to the right of the z-score 3. This can be calculated as:
P(Z > 3) = 1 - P(Z < 3)
Using the standard normal distribution table, we can find the probability associated with the z-score 3. The table will give us the probability for values up to a certain z-score, so we need to subtract it from 1.
The probability of P(Z < 3) is typically provided in the standard normal distribution table, or you can use a statistical calculator to find this value.
Let's assume that P(Z < 3) is 0.9987 (the value from the table). Subtracting this value from 1, we get:
P(Z > 3) = 1 - 0.9987
P(Z > 3) = 0.0013
Therefore, the probability that the diameter of the electric cable will exceed 0.83 is 0.0013, or 0.13%.