What is the standard deviation of a normal distribution, whose mean is 35, in which an x-value of 23 has a z-score of -1.63?
Use z-score formula and solve for standard deviation:
z = (x - mean)/sd
-1.63 = (23 - 35)/sd
Solve for sd.
To find the standard deviation of a normal distribution, we need the mean and the corresponding z-score. We are given the mean, which is 35, and the z-score of an x-value of 23, which is -1.63.
The formula to calculate the z-score is: z = (x - mean) / standard deviation
We can rearrange this equation to solve for the standard deviation:
standard deviation = (x - mean) / z
Plugging in the given values:
standard deviation = (23 - 35) / -1.63
Simplifying the calculation:
standard deviation = -12 / -1.63
Dividing:
standard deviation ≈ 7.36
Therefore, the standard deviation of the normal distribution is approximately 7.36.
To find the standard deviation of a normal distribution, we can use the formula for z-score:
z = (x - μ) / σ
where z is the z-score, x is the x-value, μ is the mean, and σ is the standard deviation.
In this case, we are given a normal distribution with a mean of 35 and an x-value of 23 that has a z-score of -1.63. We can plug in the given values to the formula and solve for the standard deviation (σ).
-1.63 = (23 - 35) / σ
To solve for σ, we need to isolate it on one side of the equation by multiplying both sides by σ:
-1.63σ = 23 - 35
Next, simplify the equation:
-1.63σ = -12
Finally, divide both sides of the equation by -1.63 to solve for σ:
σ = -12 / -1.63
σ ≈ 7.36
Therefore, the standard deviation of the given normal distribution is approximately 7.36.