Suppose x is normally distributed with a mean of 130 and a standard deviation of 25. Twenty-six percent of the values are less than what value?
123.5
114
136
146
hey i can help you
nvm.i got it!:D
To find the value below which 26% of the values fall, we can use the z-score formula and standardize the value.
The formula to calculate the z-score is given by:
z = (x - mean) / standard deviation
In this case, the mean (μ) is 130 and the standard deviation (σ) is 25. We want to find the value (x) that corresponds to the 26th percentile of the distribution.
To find the z-score corresponding to the 26th percentile, we look up the corresponding z-score from the standard normal distribution table or use a calculator.
The z-score corresponding to the 26th percentile is approximately -0.674.
Now we can use the z-score formula to find the value (x):
-0.674 = (x - 130) / 25
Rearranging the equation to solve for x:
-0.674 * 25 = x - 130
-16.85 = x - 130
x = 130 - 16.85
x ≈ 113.15
Therefore, approximately 26% of the values are less than 113.15.
Among the given options, the closest value is 114.