Question

If X is a normally distributed random variable with mean 20 and standard deviation 2 then P (X < 25) is Select one: a. P (Z < 2.5) b. P (Z < 2) c. P (Z< 1) d. P ( Z > 25)

Answer 1

P (X < 25) = P(Z < 2.5)

Step-by-step explanation:

We are given that X is a normally distributed random variable with mean 20 and standard deviation 2.

Let X = a random variable

SO, X ~ Normal($\mu=20,\sigma^{2} =2^{2}$)

The z score probability distribution for normal distribution is given by;

                                 Z = $\frac{X-\mu}{\sigma}$  ~ N(0,1)

where, $\mu$ = population mean = 20

            $\sigma$ = standard deviation = 2

Now, P (X < 25) = P( $\frac{X-\mu}{\sigma}$ < $\frac{25-20}{2}$ ) = P(Z < 2.5)

                                                       = 0.99379

The above probability is calculated by looking at the value of x = 2.5 in the z table which has an area of 0.99379.