Question

Let z denote a random variable that has a standard normal distribution. Determine each of the probabilities below. (Round all answers to four decimal places.)P(z 2.37)

Answer 1

Answer:

P(Z < 2.37) = 0.9911.

Step-by-step explanation:

We are given that Let z denote a random variable that has a standard normal distribution.

Let Z = a random variable

So, Z ~ Standard Normal(0, 1)

As we know that the standard normal distribution has a mean of 0 and variance equal to 1.

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

where, $\mu$ = mean = 0

           $\sigma$ = standard deviation = 1

Now, the probability that z has a value less than 2.37 is given by = P(Z < 2.37)

        P(Z < 2.37) = P(Z < $\frac{2.37-0}{1}$ ) = P(Z < 2.37) = 0.9911

The above probability is calculated by looking at the value of x = 2.37 in the z table which has an area of 0.9911.