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

P(Z < 2.37) = 0.9911.

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 =
`(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 <
`(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.