Problem

Find the area under the standard normal probability distribution between the following pairs of z-scores. a. $z=0$ and $z=3.00$ e. $z=-3.00$ and $z=0$ b. $z=0$ and $z=1.00$ f. $z=-1.00$ and $z=0$ c. $z=0$ and $z=2.00$ g. $z=-1.28$ and $z=0$ d. $z=0$ and $z=0.52$ h. $z=-0.52$ and $z=0$ a. The area under the standard normal probability distribution is (Round to three decimal places as needed.)

Solution

Step 1 :The area under the standard normal probability distribution between two z-scores can be found by calculating the cumulative distribution function (CDF) at the two z-scores and subtracting the smaller from the larger. The CDF of a standard normal distribution at a given z-score gives the probability that a random variable from the distribution is less than or equal to that z-score.

Step 2 :Let's consider the z-scores z1 = 0 and z2 = 3.0.

Step 3 :The area under the standard normal probability distribution between these two z-scores is approximately 0.499.

Step 4 :This means that there is a 49.9% chance that a random variable from a standard normal distribution will fall between these two z-scores.

Step 5 :Final Answer: The area under the standard normal probability distribution between \(z=0\) and \(z=3.00\) is approximately \(\boxed{0.499}\).

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