Answer :
The probability that a randomly selected man weighs less than 163 pounds is approximately 0.7422 or 74.22%.
We are given that the weights of adult males are normally distributed with a mean of 150 pounds and a standard deviation of 20 pounds.
(a) To find the probability that a randomly selected man will weigh less than 163 pounds, we need to calculate the area under the normal curve to the left of 163 pounds.
To do this, we can standardize the value using the formula for z-score:
z = (x - μ) / σ
where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.
In this case, x = 163 pounds, μ = 150 pounds, and σ = 20 pounds.
Calculating the z-score:
z = (163 - 150) / 20
z = 13 / 20
z = 0.65
Now, we can use a standard normal distribution table or a calculator to find the corresponding probability for a z-score of 0.65. The probability of a man weighing less than 163 pounds is the area to the left of the z-score of 0.65.
Looking up the z-score in the standard normal distribution table, we find that the corresponding probability is approximately 0.7422.
Therefore, the probability that a randomly selected man will weigh less than 163 pounds is approximately 0.7422, or 74.22%.
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