Answer :
Final answer:
To find the probability of a weight above 177 lb with a mean of 143 lb and a standard deviation of 29 lb, calculate the z-score and then use the z-score to determine the right-tail probability from the standard normal distribution.
Explanation:
To find the probability that the weight is above 177 lb when the weights are normally distributed with a mean (μ) of 143 lb and a standard deviation (σ) of 29 lb, we first calculate the z-score for 177 lb. The z-score is given by:
Z = (X - μ) / σ
Where X is the value we're interested in, which is 177 lb.
Z = (177 - 143) / 29
Z = 34 / 29
Z ≈ 1.1724
Now that we have the z-score, we use the standard normal distribution table, or a calculator with normal distribution capabilities, to find the probability that a single part weighs more than 177 lb, which corresponds to P(Z > 1.1724).
This gives us a probability that is usually the area to the right of the z-score on the standard normal curve. Since standard normal distribution tables typically provide the area to the left, we calculate:
P(Z > 1.1724) = 1 - P(Z < 1.1724)
Using a standard normal distribution table or calculator will give us the desired probability.
