Question

A normal distribution with a mean of 40 and a standard deviation of 5, the probability that the variable will take a value greater than 50 will be:
a) 97.70%
b) 5%
c) 2.30%
d) None of these

Answer 1

Answer:

The standard normal distribution is a normal distribution of standardized values called z-scores. A z-score is measured in units of the standard deviation.

The mean for the standard normal distribution is zero, and the standard deviation is one. What this does is dramatically simplify the mathematical calculation of probabilities. Take a moment and substitute zero and one in the appropriate places in the above formula and you can see that the equation collapses into one that can be much more easily solved using integral calculus. The transformation z = \frac{x-\mu }{\sigma } produces the distribution Z ~ N(0, 1). The value x in the given equation comes from a known normal distribution with known mean μ and known standard deviation σ. The z-score tells how many standard deviations a particular x is away from the mean.