A. In a given normal distribution, the sample mean is 75 and the sample standard deviation is 4.
Find the corresponding standard score of the following values:
1. 69
2. 85
3. 70
4. 65
To find the standard score (also called z-score) of a value in a normal distribution, you need to use the formula:
z = (x - μ) / σ
where:
- z is the standard score
- x is the given value
- μ is the mean of the distribution
- σ is the standard deviation of the distribution
Let's calculate the standard scores for the given values:
1. For the value of 69:
z = (69 - 75) / 4
= -6 / 4
= -1.5
2. For the value of 85:
z = (85 - 75) / 4
= 10 / 4
= 2.5
3. For the value of 70:
z = (70 - 75) / 4
= -5 / 4
= -1.25
4. For the value of 65:
z = (65 - 75) / 4
= -10 / 4
= -2.5
The standard scores for the given values are:
1. z = -1.5
2. z = 2.5
3. z = -1.25
4. z = -2.5
You can play around with Z table stuff at
davidmlane.com/hyperstat/z_table.html