Solve the problem.
-The lifespan for a pair of walking shoes is normally distributed with a mean of $\mu = 760,000$ steps and standard deviation of $\sigma = 17,000$ steps. If a manufacture produces 5000 pairs of these shoes, how many can be expected to last for at least 773,600 steps?
A) $\approx 1094$ pairs
B) $ \approx 1059$ pairs
C) $ \approx 1004$ pairs
D) $\approx 1159$ pairs

Question

Quizplus · Accepted Answer

To find the number of shoes expected to last at least 773,600 steps, calculate the z-score: $ z = \frac{773,600 - 760,000}{17,000} \approx 0.8 $. Using the standard normal distribution table, the probability of a z-score greater than 0.8 is approximately 0.2119. Therefore, $ 0.2119 \times 5000 \approx 1059 $ pairs.

Solve the Problem μ=760,000\mu = 760,000μ=760,000 Steps and Standard Deviation Of σ=17,000\sigma = 17,000σ=17,000

Solve the Problem $\mu = 760,000$ Steps and Standard Deviation Of $\sigma = 17,000$