Problem

Find the area under the standard normal curve between $z=1.5$ and $z=2.5$. Round to two decimals. Find the $z$-score for which the area under the standard normal curve to its right is 0.70 . Round to one decimal.

Solution

Step 1 :The first question is asking for the area under the standard normal curve between two z-scores. The area under the standard normal curve represents the probability that a random variable from a normal distribution falls within a certain range. This can be calculated using the cumulative distribution function (CDF) of the standard normal distribution. The CDF at a certain point is the area under the curve to the left of that point. Therefore, to find the area between two points, we can subtract the CDF at the lower point from the CDF at the higher point.

Step 2 :The second question is asking for the z-score such that the area to the right of it under the standard normal curve is 0.70. This is equivalent to finding the z-score such that the area to the left of it is 1 - 0.70 = 0.30. This can be found using the inverse of the CDF, also known as the quantile function or the percent-point function.

Step 3 :The area under the standard normal curve between \(z=1.5\) and \(z=2.5\) is \(\boxed{0.06}\).

Step 4 :The \(z\)-score for which the area under the standard normal curve to its right is 0.70 is \(\boxed{-0.5}\).

From Solvely APP
Source: https://solvelyapp.com/problems/20325/

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