Let X be a normally distributed random variable with a mean of 20 and a standard deviation of 2.25. Using Excel, find the proportion of the values of X that are less than 21.

Answer: The normal distribution is the most important distribution. It describes well the

distribution of random variables that arise in practice, such as the heights or weights

of people, the total annual sales of a firm, exam scores etc. Also, it is important for the

central limit theorem, the approximation of other distributions such as the binomial,

etc.

• We say that a random variable X follows the normal distribution if the probability

density function of X is given by

f (x) = 1

σ

√

2π

e

- 1

2

(

x-µ

σ

)

2

, - ∞ < x < ∞

This is a bell-shaped curve.

• We write X ∼ N (µ, σ). We read: X follows the normal distribution (or X is normally

distributed) with mean µ, and standard deviation σ.