Answer :
Final answer:
The solution involves calculating the z-score for a weight of 108 pounds based on the given mean and standard deviation, and then finding the corresponding probability from a z-table to determine the likelihood of a woman weighing less than 108 pounds.
Explanation:
The question asks us to find the probability that the weight of a randomly selected woman is below 108 pounds, given a normal distribution where the mean (μ) is 143 pounds and the standard deviation (σ) is 29 pounds. To solve this, we use the z-score formula:
Z = (X - μ) / σ
where,
X = 108 pounds (woman's weight we're interested in),
μ = 143 pounds (mean weight), and
σ = 29 pounds (standard deviation).
Substituting the given values:
Z = (108 - 143) / 29
Z = -35 / 29
Z = -1.21
After calculating the z-score, we refer to the standard normal distribution table (z-table) to find the probability that corresponds to the calculated z-score. The probability for Z < -1.21 would give us the likelihood that a woman weighs less than 108 pounds.
In the context of this problem, normal distribution and computation of a z-score are key concepts used to find the probability.
