Let z be a random variable with a standard normal distribution, P(-1.9<=z<=2.1)
I assume that you are talking about Z scores, scores in terms of standard deviations. However, I am not sure what your question is.
Possibly it would help to find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to those Z scores.
To find the probability P(-1.9 ≤ z ≤ 2.1) for a standard normal distribution, you can use a standard normal distribution table or a calculator.
Here's how you can use a standard normal distribution table:
1. Start by finding the probabilities for the individual values -1.9 and 2.1 separately.
- Look up the value -1.9 in the table. The table will give you the area to the left of -1.9 in the standard normal distribution. Let's call this probability A.
- Look up the value 2.1 in the table. The table will give you the area to the left of 2.1 in the standard normal distribution. Let's call this probability B.
2. Next, calculate the probability for the interval -1.9 ≤ z ≤ 2.1. Since the standard normal distribution is symmetric, the probability P(-1.9 ≤ z ≤ 2.1) is equal to B - A.
For example, if A = 0.0287 and B = 0.9821, then the probability P(-1.9 ≤ z ≤ 2.1) is approximately 0.9821 - 0.0287 = 0.9534.
Keep in mind that the exact values in the table may differ based on the specific version of the table or calculator you use.