For a normal distribution, identify the z-score location that would separate the distribution into sections so that there is:
a)60% in the body on the right-hand side
b)90% in the body on the left-hand side
60% is to the right of z = -0.25
90% is to the left of z = +1.28
"z" is (x-x(mean))/{standard deviation)
You need a table of the error function or normal distribution to do this kind of problem.
a) To find the z-score location that separates the distribution into sections with 60% in the body on the right-hand side, we need to find the z-score that corresponds to the cumulative probability of 0.6.
Using a standard normal distribution table or calculator, we can find that the z-score for a cumulative probability of 0.6 is approximately 0.2533.
Therefore, the z-score location that separates the distribution with 60% in the body on the right-hand side is approximately 0.2533.
b) To find the z-score location that separates the distribution into sections with 90% in the body on the left-hand side, we need to find the z-score that corresponds to a cumulative probability of 0.9.
Using a standard normal distribution table or calculator, we can find that the z-score for a cumulative probability of 0.9 is approximately 1.2816.
Therefore, the z-score location that separates the distribution with 90% in the body on the left-hand side is approximately 1.2816.
To find the z-score location that separates a normal distribution into specific sections, we can use a standard normal distribution table or a statistical calculator. The z-score represents the number of standard deviations a value is from the mean of the distribution.
a) To determine the z-score location that separates 60% of the distribution to the right-hand side, we need to find the z-score at the cumulative area of 0.40 (1 - 0.60). This means we are looking for the z-score that corresponds to the 40th percentile.
Using a standard normal distribution table or a statistical calculator, we can find that a z-score of approximately 0.25 separates 60% of the distribution to the right-hand side.
b) To identify the z-score location that separates 90% of the distribution to the left-hand side, we need to find the z-score at the cumulative area of 0.90. This means we are looking for the z-score that corresponds to the 90th percentile.
Using a standard normal distribution table or a statistical calculator, we can find that a z-score of approximately -1.28 separates 90% of the distribution to the left-hand side.
Note: The specific values may vary slightly due to rounding or table accuracy, but these approximate values should be sufficient for most practical purposes.