Assume x is normally distributed with mean µ= 15 and standard deviation α= 3-. Use the approximate areas beneath the normal curve, as discussed in this section, to answer the following questions. Find P (X ≥15)-
A) 0.50
B) 0.16
C) 0.34
D) 0.84
if you are studying statistics, I find it totally unjustified and unacceptable that you would post this question.
If you have a normal distribution, and it said there is, and the mean is 15, how many would be below this mean and how many would be above this mean ??
To find P(X ≥ 15) using the normal distribution, we need to convert the value of 15 into a standard score or z-score.
The formula for calculating the z-score is:
z = (x - µ) / α
where x is the given value, µ is the mean, and α is the standard deviation.
In this case, x = 15, µ = 15, and α = 3.
Plugging these values into the formula, we get:
z = (15 - 15) / 3 = 0 / 3 = 0
The z-score is zero because the value of 15 is equal to the mean.
Now, we need to find the probability associated with the area to the right of the z-score of 0. This is equivalent to finding the area under the normal curve to the right of the mean.
We can use a standard normal distribution table or a statistical software to find the corresponding probability.
Using a standard normal distribution table, we look for the value closest to 0 (or -0) in the z-score column. The corresponding probability is 0.5000. Since we are interested in the area to the right of the mean, we subtract this probability from 1:
P(X ≥ 15) = 1 - 0.5000 = 0.5000
Therefore, the answer is A) 0.50.