Question

Select the correct answer. consider a normally distributed data set with a mean of 154 and a standard deviation of 9.8. if one of the observed values is 176, what is the z score?

1. The correct is c. +2.24.
The z score obtained by the normal distribution is 2.24.

### What is normal distribution?

The normal distribution is formally known as that of the Gaussian distribution, but the name “normal” was used when scientific papers in the nineteenth century demonstrated that numerous natural phenomena claimed to “deviate normally” as from mean.
The naturalist Sir Francis Galton popularized the concept of “normal variability” as the “normal curve” in his 1889 study, Natural Inheritance.
According to the question,
The formula for finding z-value from normal distribution is;
z = (x – μ) / σ
Where, x is the original score ( = 176)
μ is the mean. (= 154)
σ is the standard deviation (= 9.8)
Thus,
z = (176 – 154) / 9.8
z = 2.245
Therefore, z-score obtained by method of normal distribution is 2.24.
To know more about the normal distribution, here
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The complete question is-
Select the correct answer. consider a normally distributed data set with a mean of 154 and a standard deviation of 9.8. if one of the observed values is 176, what is the z score?
a. +3.36
b. -2.24
c. +2.24
d. -22.00
e. +22.00