14. Assume that the random variable X is normally distributed, with mean of 100 and standard deviation of 20. Compute the probability P(X> 116).
Z = (score-mean)/SD = (116-100)/20 = ?
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability.
To calculate the probability P(X > 116) for a normally distributed random variable, with mean of 100 and standard deviation of 20, we can use the standardized z-score formula and table.
The z-score formula is:
z = (x - μ) / σ
where x is the value we want to find the probability for (116 in this case), μ is the mean (100), and σ is the standard deviation (20).
Substituting the given values into the formula:
z = (116 - 100) / 20 = 0.8
We need to find the probability of X being greater than 116, which is the same as finding the probability to the right of the z-score 0.8 on the standard normal distribution table.
Using the table or a z-score calculator, we can find the area/probability to the left of 0.8 in the standard normal distribution. From the table, we can see that the area to the left of 0.8 is 0.7881.
Since we are looking for the probability to the right of 0.8, we subtract 0.7881 from 1: 1 - 0.7881 = 0.2119.
So, the probability P(X > 116) is 0.2119 or 21.19%.