Question

What value of z divides the standard normal distribution so that half the area is on one side and half is on the other? round your answer to two decimal places?

Answer 1

The value of $Z$ is $\boxed{0.00}$ that divides the standard normal distribution so that half the area is on one side and half is on the other.

Further explanation:

The normal distribution that has mean zero and variance one is known as standard normal distribution.

The random variable $X$ follows standard normal distribution with mean zero and variance one.

$\boxed{X \sim N\left( {0,1} \right)}$

Then the value of $Z$ can be obtained as,

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

Calculation:

The normal distribution is symmetric.

The standard normal distribution is bell shaped curve and it also a symmetric curve.

From the standard normal table or $Z$-table the value that divides the data into two equal half is $\boxed{0.00}$.

The $50\%$ data lies above zero and $50\%$ data lies below zero.

Hence, the value of $Z$ is $\boxed{0.00}$ that divides the standard normal distribution so that half the area is on one side and half is on the other.

Learn more:

1. Learn more about normal distribution brainly.com/question/12698949

2. Learn more about standard normal distribution brainly.com/question/13006989

3. Learn more about confidence interval of mean brainly.com/question/12986589

Answer details:

Grade: College

Subject: Statistics

Chapter: Normal distribution

Keywords: Z-score, Z-value, standard normal distribution, standard deviation, criminologist, test, measure, probability, low score, mean, repeating, indicated, normal distribution, percentile, percentage, undesirable behavior, proportion, empirical rule.

Answer 2

A standard normal distribution is a normal distribution that has a mean of 0 and standard deviation of 1. A z value of 0.00 divides the standard normal distribution into two equal halves with 50% on each side.