Final answer:
The standard deviation of a normal distribution with a mean of 50 where 25% of the values are above 60 is calculated using the z-score formula. The resulting standard deviation is 14.83, which is closest to option C. 14.93.
Step-by-step explanation:
To determine the standard deviation when it is known that 25% of the values are above 60 in a normal distribution with a mean of μ=50, we must use the concept of z-scores. The 75th percentile, which is the point below which 75% of the observations lie, corresponds to a z-score of approximately 0.674 (from z-score tables). Since 25% of the values are above 60, 60 is the 75th percentile of this distribution.
Using the formula for the z-score:
Z = (X - μ) / σ,
where Z is the z-score, X is the value (60 in this case), μ is the mean (50), and σ is the standard deviation.
Plugging in the values:
0.674 = (60 - 50) / σ
Solving for σ:
σ = (60 - 50) / 0.674
σ = 14.83
Thus, the standard deviation of the normal model is 14.83, which comes closest to option C. 14.93.
We can now confidently mention that the correct option is C. 14.93.