Here the population standard deviation is 0.60 degree F. If a sample of 36 adults is randomly selected, that results in a sample standard deviation of 0.60 degree F divided by the square root of 36: 0.10 degree F.
The probability in question is the area under the standard normal probability distribution between 98.4 degree F and infinity, and intuitively you can detect that this will be more than 0.5 (corresponding to 50%).
Convert 98.4 degrees F to a z-score, using the sample standard deviation (0.10 degree F). That z score is
98.4-98.6
z = -------------- = -0.20/0.10 = -2
0.10
We need to determine the area under the standard normal curve to the right of z=-2. Use a table of z-scores to do this, or use your calculator's built-in probability functions. My result is 98.21% (corresponding to an area of 0.9821).
With my calculator I can find this probability using the following command:
normalcdf(-2,100000,0.10).
