Answer :
The probability a sample of 36 randomly selected males will have an average weight between 165 and 175 pounds is 0.8708.
Given the average weight of an adult male in one state is 172 pounds with a standard deviation of 16 pounds. We have to calculate the probability a sample of 36 randomly selected males will have an average weight between 165 and 175 pounds.The mean of the sample is μ = 172 pounds.The standard deviation of the population is σ = 16 pounds.Sample size is n = 36.We know that the formula for calculating z-score is:
z = (x - μ) / (σ / sqrt(n))
For x = 165 pounds:
z = (165 - 172) / (16 / sqrt(36))
z = -2.25
For x = 175 pounds:
z = (175 - 172) / (16 / sqrt(36))
z = 1.125
Now we have to find the area under the normal curve between these two z-scores using the z-table. Using the table, we find that the area to the left of -2.25 is 0.0122, and the area to the left of 1.125 is 0.8708. Therefore, the area between these two z-scores is:
0.8708 - 0.0122 = 0.8586This is the probability a sample of 36 randomly selected males will have an average weight between 165 and 175 pounds. Therefore, the correct response is 0.8708.
Therefore, the probability a sample of 36 randomly selected males will have an average weight between 165 and 175 pounds is 0.8708.
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