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Aliun [14]
1 year ago
6

Find the value of z such that 0.8664 of the area lies between −z and z. Round your answer to two decimal places.

Mathematics
1 answer:
Archy [21]1 year ago
8 0

Using the normal distribution, the value of z is of z = 1.5.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

Z = \frac{X - \mu}{\sigma}

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

For this problem, considering the symmetry of the normal distribution, the area above the mean is given by:

0.8664/2 = 0.4332.

Hence <u>z has a p-value of 0.5  + 0.4332 = 0.9332</u>, hence the value of z is z = 1.5.

More can be learned about the normal distribution at brainly.com/question/24537145

#SPJ1

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