Question

Average weight of males in the age bracket of 20−39 is 199 pounds. Assume population standard deviation of weight of this group of males is 15.5 pounds. You obtain a random sample of 40 males in this age bracket. 14 What is the probability that the sample mean is greater than 202 ?

a 0.1105
b 0.1023
c 0.0947
d 0.0877
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Answer 1

The probability that the sample mean is greater than 202 pounds is approximately 84.98%.

Step-by-step explanation:

To find the probability that the sample mean is greater than 202 pounds, we need to calculate the z-score and use the standard normal distribution table. The z-score is calculated as (sample mean - population mean) / (population standard deviation / sqrt(sample size)). In this case, the z-score is (202 - 199) / (15.5 / sqrt(40)) = 1.03. Using the standard normal distribution table, we can find the probability associated with a z-score of 1.03, which is approximately 0.1502. However, we need to find the probability of the sample mean being greater than 202, so we can subtract the probability of the sample mean being less than or equal to 202 from 1. The probability that the sample mean is greater than 202 is approximately 1 - 0.1502 = 0.8498, or 84.98%.a