find area under the standard normal curve A). p(z>0.58) B. p(-1.10<z<0)C. P(-1.60>=<z<2.09)
To find the area under the standard normal curve for the given probabilities, you can use a standard normal distribution table or a calculator with a normal distribution function. Here's how you can find the answers to each part of your question:
A) To find the area to the right of z = 0.58, we need to find the probability p(z > 0.58).
Option 1: Using a Standard Normal Distribution Table
Look for the z-score closest to 0.58 in the table. In this case, it would be 0.59. The table gives the area to the left of the z-score, so we need to subtract the value in the table from 1 to find the area to the right.
Looking up the z-score of 0.59 in the table, we find that the corresponding area is 0.7224. Subtracting this value from 1, we get:
Area to the right = 1 - 0.7224 = 0.2776
Option 2: Using a Calculator or Software
You can use a calculator or software that has a normal distribution function to calculate the area to the right of z = 0.58 directly. The result should be 0.2776.
B) To find the area between z = -1.10 and z = 0, we need to find the probability p(-1.10 < z < 0).
Option 1: Using a Standard Normal Distribution Table
Look up the z-scores -1.10 and 0 in the table. The table gives the area to the left of the z-score, so we subtract the area for z = -1.10 from the area for z = 0.
Looking up the z-score of -1.10 in the table, we find that the corresponding area is 0.1357.
Looking up the z-score of 0 in the table, we find that the corresponding area is 0.5000.
Subtracting 0.1357 from 0.5000, we get:
Area between -1.10 and 0 = 0.5000 - 0.1357 = 0.3643
Option 2: Using a Calculator or Software
Using a calculator or software, you can directly calculate the area between z = -1.10 and z = 0. The result should be 0.3643.
C) To find the area between z = -1.60 and z = 2.09, we need to find the probability p(-1.60 < z < 2.09).
Option 1: Using a Standard Normal Distribution Table
Look up the z-scores -1.60 and 2.09 in the table. The table gives the area to the left of the z-score, so we subtract the area for z = -1.60 from the area for z = 2.09.
Looking up the z-score of -1.60 in the table, we find that the corresponding area is 0.0548.
Looking up the z-score of 2.09 in the table, we find that the corresponding area is 0.9810.
Subtracting 0.0548 from 0.9810, we get:
Area between -1.60 and 2.09 = 0.9810 - 0.0548 = 0.9262
Option 2: Using a Calculator or Software
Using a calculator or software, you can directly calculate the area between z = -1.60 and z = 2.09. The result should be 0.9262.
To find the area under the standard normal curve, we will use a z-table. The z-table provides the cumulative probability for values up to a given z-score.
A) To find P(z > 0.58):
First, we need to find the area to the left of z = 0.58 on the z-table.
Looking up 0.58 in the z-table, we find the value of 0.7186.
Since we want the area to the right of z = 0.58, we subtract 0.7186 from 1:
Area = 1 - 0.7186
Area ≈ 0.2814
B) To find P(-1.10 < z < 0):
First, we need to find the area to the left of z = -1.10 on the z-table.
Looking up -1.10 in the z-table, we find the value of 0.1357.
Next, we need to find the area to the left of z = 0 on the z-table.
Looking up 0 in the z-table, we find the value of 0.5000.
To find the area between these two z-values, we subtract the smaller area from the larger area:
Area = 0.5000 - 0.1357
Area ≈ 0.3643
C) To find P(-1.60 ≤ z ≤ 2.09):
First, we need to find the area to the left of z = -1.60 on the z-table.
Looking up -1.60 in the z-table, we find the value of 0.0548.
Next, we need to find the area to the left of z = 2.09 on the z-table.
Looking up 2.09 in the z-table, we find the value of 0.9814.
To find the area between these two z-values, we subtract the smaller area from the larger area:
Area = 0.9814 - 0.0548
Area ≈ 0.9266
So, the areas under the standard normal curve are:
A) p(z > 0.58) ≈ 0.2814
B) p(-1.10 < z < 0) ≈ 0.3643
C) p(-1.60 ≤ z ≤ 2.09) ≈ 0.9266