Question

Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)

P(−0.53 ≤ z ≤ 2.04) =

Answer 1

SOLUTION:

From given data,

Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.) P(−0.53 ≤ z ≤ 2.04)

The value of  P(−0.53 ≤ z ≤ 2.04) is obtined as shown below:

The required value is,

P(−0.53 ≤ z ≤ 2.04) = P( z ≤ 2.04) - P( z ≤ −0.53)

From the standard Normal distribution table , the area to the left of z=2.04 is 0.9793 and

The area of left of z = -0.53 is 0.2981 . Then

P(−0.53 ≤ z ≤ 2.04) = P( z ≤ 2.04) - P( z ≤ −0.53)

= 0.9793 -  0.2981

= 0.6812

The value of P(−0.53 ≤ z ≤ 2.04) =  0.6812