1.

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»

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.



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