Consider the Standard Normal curve:
(a) Find the area between z = -0.45 and z = 1.45
(b) Find the value of z such that the area to the right of z is 1.5%.
lots of z table stuff here:
http://davidmlane.com/hyperstat/z_table.html
To find the area between two values on the standard normal curve, we use the standard normal distribution table or a statistical software. Let's go through the steps for each part of the question.
(a) To find the area between z = -0.45 and z = 1.45, we can look up the area corresponding to each value in the standard normal distribution table and then subtract the smaller area from the larger area.
From the table, we find that the area to the left of z = -0.45 is 0.3264, and the area to the left of z = 1.45 is 0.9265.
Therefore, the area between z = -0.45 and z = 1.45 is:
0.9265 - 0.3264 = 0.6001
(b) To find the value of z such that the area to the right of z is 1.5%, we can use the standard normal distribution table by looking for the closest value to 1.5% (0.015) and finding the corresponding z-value.
From the table, we find that the closest value to 0.015 is 0.0149. The corresponding z-value is approximately 2.17.
Therefore, the value of z such that the area to the right of z is 1.5% is approximately 2.17.
To find the area between two z-scores on the Standard Normal curve, you can use a Standard Normal distribution table or a statistical calculator.
(a) Finding the area between z = -0.45 and z = 1.45:
1. Using a Standard Normal distribution table:
- Look up the z-values -0.45 and 1.45 in the table. The table will provide the corresponding area under the curve for each z-value.
- Subtract the area corresponding to z = -0.45 from the area corresponding to z = 1.45 to get the desired area between the two z-scores.
2. Using a statistical calculator:
- Calculate the cumulative probability for z = -0.45 and z = 1.45. The cumulative probability represents the area under the curve from negative infinity up to a specific z-value.
- Subtract the cumulative probability corresponding to z = -0.45 from the cumulative probability corresponding to z = 1.45 to get the desired area between the two z-scores.
(b) Finding the value of z for which the area to the right is 1.5%:
1. Using a Standard Normal distribution table:
- Look for the closest area less than 1.5% (0.015) in the cumulative probability column of the table.
- Identify the corresponding z-value in the z-score column.
2. Using a statistical calculator:
- Calculate the inverse cumulative probability (also known as the quantile function) for the area of 1 - 0.015 = 0.985 (since we are interested in the area to the right of z).
- The resulting z-value will be the desired answer.
Note that the answers obtained from the table and calculator may have slight variations due to rounding or interpolation methods used.