what proportion of a normaql distribution is located between each of the following z- score boundaries?
a. z= -0.50 and z = +0.50
b. z= - 0.90 and z= +0.90
c. z= -1.50 and z= +1.50
How will I know the question has been answered
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions between these Z scores.
imsu
a. To find the proportion of a normal distribution between z = -0.50 and z = +0.50, we need to calculate the area under the curve within this range. This can be done by finding the cumulative probability associated with each z-score and finding the difference between them.
Using a standard normal distribution table or a calculator, we can find that the cumulative probability for z = -0.50 is approximately 0.3085 and the cumulative probability for z = +0.50 is approximately 0.6915.
Therefore, the proportion of the normal distribution located between z = -0.50 and z = +0.50 is approximately 0.6915 - 0.3085 = 0.383.
b. Similarly, to find the proportion of a normal distribution between z = -0.90 and z = +0.90, we can find the cumulative probabilities for each z-score and calculate the difference.
The cumulative probability for z = -0.90 is approximately 0.1841, and the cumulative probability for z = +0.90 is approximately 0.8159.
Thus, the proportion between z = -0.90 and z = +0.90 is approximately 0.8159 - 0.1841 = 0.632.
c. Lastly, to find the proportion of a normal distribution between z = -1.50 and z = +1.50, we calculate the cumulative probabilities for each z-score and find the difference.
The cumulative probability for z = -1.50 is approximately 0.0668, and the cumulative probability for z = +1.50 is approximately 0.9332.
Consequently, the proportion between z = -1.50 and z = +1.50 is approximately 0.9332 - 0.0668 = 0.8664.
So, the proportion for each boundary is:
a. approximately 0.383
b. approximately 0.632
c. approximately 0.8664
To find the proportion of a normal distribution located between given z-score boundaries, you can use a standard normal distribution table (also called a z-table) or a statistical software program. Here's how you can find the answers:
a. z = -0.50 and z = +0.50:
The z-score represents the number of standard deviations a data point is from the mean in a normal distribution. Since the z-scores are symmetrical around zero, the proportion between z = -0.50 and z = +0.50 will be the same as the proportion between z = 0 and z = +0.50.
Using a z-table or statistical software, you can look up the proportion associated with z = 0 (which is the mean) and the proportion associated with z = +0.50. The difference between these two proportions will give you the proportion between z = -0.50 and z = +0.50.
b. z = -0.90 and z = +0.90:
Similar to part a, you can use a z-table or statistical software to find the proportion associated with z = 0 and the proportion associated with z = +0.90. The difference between these two proportions will give you the proportion between z = -0.90 and z = +0.90.
c. z = -1.50 and z = +1.50:
Again, you can use a z-table or statistical software to find the proportion associated with z = 0 and the proportion associated with z = +1.50. The difference between these two proportions will give you the proportion between z = -1.50 and z = +1.50.
Remember, when using a z-table, the values correspond to the proportions in the body of the standard normal distribution curve. If needed, you may need to use the complementary rule (subtracting the value from 1) to find the proportion in the desired area, depending on the orientation of the table or software program you are using.
Once you have calculated the proportions between the given z-score boundaries, you can provide the answers in your response.