Final answer:
To find the probability of x being greater than 185.61 in a normal distribution with a mean of 206 and a standard deviation of 20.6, calculate the z-score and find the area under the standard normal distribution curve to the right of the z-score. The probability is 0.8413, or 84.13%.
Step-by-step explanation:
To find the probability of x being greater than 185.61 in a normal distribution with a mean of 206 and a standard deviation of 20.6, we need to calculate the z-score and find the area under the standard normal distribution curve to the right of the z-score.
First, we calculate the z-score using the formula:
z = (x - mean) / standard deviation = (185.61 - 206) / 20.6 = -1
The area to the right of the z-score can be found using a standard normal distribution table or a calculator. The area to the left of z=-1 is 0.1587. Therefore, the probability of x being greater than 185.61 is 1 - 0.1587 = 0.8413, or 84.13%.