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what is the normal distribution probability where x is more than 185.61 for a mean of 206, and standard deviation of 20.6

User Scottt
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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%.

User GoldenJam
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