Answer :
Answer:
The z-score for a data value of 121 is -2.29.
Step-by-step explanation:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 137, \sigma = 7[/tex]
Find the z-score for a data value of 121.
This is Z when X = 121. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{121 - 137}{7}[/tex]
[tex]Z = -2.29[/tex]
The z-score for a data value of 121 is -2.29.
Answer:
[tex]-2.29[/tex].
Step-by-step explanation:
We have been given that a normal distribution has a mean of 137 and a standard deviation of 7. We are asked to find the z-score corresponding to data value 121.
We will use z-score formula to solve our given problem.
[tex]z=\frac{x-\mu}{\sigma}[/tex], where,
z = Z-score,
x = Sample score,
[tex]\mu[/tex] = Mean,
[tex]\sigma[/tex] = Standard deviation.
Upon substituting our given values in above formula, we will get:
[tex]z=\frac{121-137}{7}[/tex]
[tex]z=\frac{-16}{7}[/tex]
[tex]z=-2.2857142857[/tex]
Upon rounding to two decimal places, we will get:
[tex]z\approx -2.29[/tex]
Therefore, z-score corresponding to data value 121 would be [tex]-2.29[/tex].