Assume normal distributions in the following exercises. Find the value of z. An estimated 86% of the scores are to the left of z.

Alexus Deleon 2022-09-21 Answered
Assume normal distributions in the following exercises. Find the value of z. An estimated 86% of the scores are to the left of z.
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Answers (1)

Abram Jacobson
Answered 2022-09-22 Author has 8 answers
The z-score represents the number of standard deviations between an observation and the mean. Whatever scale is used for on a normal curve, we can associate a value of z with each value of x.
We use z to find the area under the normal curve between two scores. To do so, we use the standard normal table. The table gives area between the mean and a z-score for selected z-scores.So as 86% of the result is to the left of z, and the normal distribution is symmetric with the area below the normal curve 1, is 0.5 on the left and right sides of the mean. This actually means that between z and the mean is 36%, so the area between z and the mean is 0.42. Using the table of standard normal distribution we can see that the area A = 0.36 corresponds to z = 1.09.
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