The value of [tex]z[/tex] is [tex]\boxed{1.17}[/tex] for the value of the cumulative standardized normal distribution at [tex]z[/tex] is [tex]0.8770[/tex].
Further explanation:
Given:
The cumulative standardized normal distribution is [tex]0.8770[/tex].
Concept used:
The normal distribution that has mean zero and variance one is called 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 [tex]z[/tex] can be obtained as,
[tex]\boxed{Z = \frac{{X - \mu }}{\sigma }}[/tex]
Calculation:
The normal distribution is symmetric.
The standard normal distribution is bell shaped curve and it also a symmetric curve.
The cumulative standardized normal distribution is [tex]0.8770[/tex] it is area under the curve.
The probability of a number less than [tex]z[/tex] value is [tex]0.8770[/tex].
From the [tex]z[/tex] table the approximate value of the [tex]z[/tex] is [tex]\boxed{1.17}[/tex].
Kindly refer to the image attached.
Learn more:
1. Learn more about normal distribution https://brainly.com/question/12698949
2. Learn more about standard normal distribution https://brainly.com/question/13006989
3. Learn more about confidence interval of mean https://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., cumulative standardized normal distribution.
