According to a study done by the Gallup organization, the proportion of Americans who are satisfied with the way things are going in their lives is 0.82. What is the probability the sample proportion who are satisfied with the way things are going in their life is greater than 0.85

Complete Question

According to a study done by the Gallup organization, the proportion of Americans who are satisfied with the way things are going in their lives is 0.82. Suppose a random sample of 100 Americans is asked "Are you satisfied with the way things are going in your life?"

What is the probability the sample proportion who are satisfied with the way things are going in their life is greater than 0.85

The probability is  

Step-by-step explanation:

From the question we are told that

   The population proportion is

   The value considered is  x  =  0.85

     The  sample size is  n = 100

The standard deviation for this population proportion is evaluated as

substituting values

Generally the probability that probability the sample proportion who are satisfied with the way things are going in their life is greater than x is mathematically represented as

Where   is  equal to Z (the  standardized value of X ) so  

substituting values

from the standardized normal distribution table is  0.21745

So