Step-by-step explanation:
z = (specific score - mean) / standard deviation
in our case
z = (105 - 101)/4.2 = 4/4.2 = 0.952380952... ≈ 0.95
as z-tables usually round the z-scores to hundredths.
The z-score of the normal distribution is 0.95.
A probability distribution which is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution.
It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean. The normal distribution shows as a "bell curve" on a graph.
Z-score: A Z-score is just a metric that quantifies how closely a value relates to a mean of a set of values. Standard deviations from of the mean are used to measure Z-score.
A Z-score of zero means the data point is actually score is the same as the mean score.
The formula for z-score is-
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
Z = standard score
x is observed value = 105
[tex]\mu[/tex] is mean of the sample 101.
[tex]\sigma[/tex] is standard deviation of the sample 4.2.
Substitute all the values in the z-score formula;
z = ( 105 - 101)/4.2
z = 0.9523..
z = 0.95
Therefore, the z-score the given normal distribution is 0.95.
To know more about characteristics of a normal distribution, here
https://brainly.com/question/23418254
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