A normal distribution has a standard deviation of 25, and about 2.3% values are below 10. Find the mean for this distribution.
A) 60
B) 70
C) 40
D) 50
E) 10

Question

Quizplus · Accepted Answer

The mean of the distribution can be found using the Z-score formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation. Given that about 2.3% of values are below 10, this corresponds to a Z-score of approximately -2 (since 2.3% is close to the tail end of a normal distribution, which corresponds to a Z-score of about -2). Plugging in the values: -2 = (10 - μ) / 25. Solving for μ gives μ = 10 + 2(25) = 60.

A Normal Distribution Has a Standard Deviation of 25, and About