Question

According to the empirical (69-95-99.7) rule, if a random variable z has a standard normal distribution, then approximately 95%

Answer 1

Using z-scores, it is found that the value of z is z = 1.96.

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Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula, which for a measure X, in a distribution with mean $\mu$ and standard deviation $\sigma$, is given by:  

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

• It measures how many standard deviations the measure is from the mean.
• Each z-score has an associated p-value, which is the percentile.

• The normal distribution is symmetric, which means that the middle 95% is between the 2.5th percentile and the 97.5th percentile.
• The 2.5th percentile is Z with a p-value of 0.025, thus Z = -1.96.
• The 97.5th percentile is Z with a p-value of 0.975, thus Z = 1.96.
• Thus, the value of Z is 1.96.

A similar problem is given at brainly.com/question/16965597