Question

Assuming X is a normally distributed random variable with = 130 and = 13, find P(X > 143). (Round your answer to 4 decimal places.)

Answer 1

To find the probability that X is greater than 143, we need to standardize the value of 143 using the mean and standard deviation of the normal distribution. The standardized value, or z-score, can then be used to find the corresponding probability using a z-table or calculator. The probability that X is greater than 143 is approximately 0.1587.

Step-by-step explanation:

To find the probability that X is greater than 143, we need to calculate the area under the normal distribution curve to the right of 143. Since we don't have a standard normal distribution, we need to standardize the value of 143 using the mean (130) and standard deviation (13). The standardized value, which is the z-score, can then be used to find the corresponding probability using a z-table or a calculator.

Using the z-score formula: z = (x - μ) / σ, where x is the value (143), μ is the mean (130), and σ is the standard deviation (13), we can calculate the z-score: z = (143 - 130) / 13 = 1.

Looking up the probability associated with a z-score of 1 in a standard normal distribution table or using a calculator, we find that P(X > 143) = 0.1587. Therefore, the probability that X is greater than 143 is approximately 0.1587.