Question

Find the area under the standard normal curve between the given z-values. Round your answer to four decimal places, if necessary.Z₁ =1.58, 22 = 1.58Answer

Answer 1

The area under standard normal curve for the variable is 0.8859

Finding the area under standard normal curve for the variable

From the question, we have the following parameters that can be used in our computation:

z = -1.58 to 1.58

For a standard normal Distribution, we have that

Mean = 1

Standard deviation = 0

This means that

Area = P(-1.58 < z < 1.58)

Using the Normal Distribution Table. we hae the following readings

P(-1.58 < z < 1.58) = 0.8859

This means that

Area = 0.8859

Hence, the area under standard normal curve is 0.8859

Answer 2

To find the area under the curve between two given z-scorers, having a z-table would be handy.

Remember that the z-table gives the area to the left of a given z-score.

For z = -1.58, the corresponding area according to the z-table is 0.05705.

Meanwhile, for z = 1.58, the corresponding area is 0.94295.

Again, these areas are to the left of the z-score given. So, if we are to find the area between them, we will have to subtract 0.94295 - 0.05705.

`\begin{gathered} Area=0.94295-0.05705 \\ Area=0.8859 \end{gathered}`

The answer is 0.8859.