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Compute the z-score corresponding to each of the following
Chapter , Problem 90E(choose chapter or problem)
Compute the z-score corresponding to each of the following values of x:
a. \(x=40, s=5, \bar{x}=30\)
b. \(x=90, \mu=89, \sigma=2\)
c. \(\mu=50, \sigma=5, x=50\)
d. \(s=4, x=20, \bar{x}=30\)
e. In parts a–d, state whether the z-score locates x within a sample or a population.
f. In parts a–d, state whether each value of x lies above or below the mean and by how many standard deviations.
Questions & Answers
QUESTION:
Compute the z-score corresponding to each of the following values of x:
a. \(x=40, s=5, \bar{x}=30\)
b. \(x=90, \mu=89, \sigma=2\)
c. \(\mu=50, \sigma=5, x=50\)
d. \(s=4, x=20, \bar{x}=30\)
e. In parts a–d, state whether the z-score locates x within a sample or a population.
f. In parts a–d, state whether each value of x lies above or below the mean and by how many standard deviations.
ANSWER:Step 1 of 7
Here, for the given values of x,s and \(\bar{x}\) we have to find the z score.
Using the z score obtained we have to answer the given questions.
The z score is given by
\(\mathrm{Z}=\frac{x-\bar{x}}{s}\)
Or
\(\mathrm{Z}=\frac{x-\mu}{\sigma}\)