Assume normal distributions in the following exercises. Find the value of z. The probability that a score is between z and -z is 0.82.

Ilnaus5

Ilnaus5

Answered question

2022-09-24

Assume normal distributions in the following exercises. Find the value of z. The probability that a score is between z and -z is 0.82.

Answer & Explanation

Nathalie Rivers

Nathalie Rivers

Beginner2022-09-25Added 7 answers

The z-score represents the number of standard deviations between an observation and the mean. Whatever scale is used for c on a normal curve, we can associate a value of z with each value of z.
We use z to find the area under the normal curve between the two results. Io do this, we use a standard normal table. The table gives the area between the mean and z -score for the selected z -results. Since the 82% result is between z and -z, and the normal distribution is symmetric and the area under the normal curve is 1, is 0.5 between the mean and z and 0.5 between z and mean values. This actually means that between 2 and the mean is 41%, the result between and between-2 and the mean 41% of the result. So the area between z and the mean is 0.41. Using the standard normal distribution table, we can see that the area A = 0.41 corresponds to z = 1.35.

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