Question

Automobile Workers: A worker in the automobile industry works an average of 43.6 hours per week. If the distribution is approximately normal with a standard deviation of 1.3 hours, what is the probability that a randomly selected automobile worker works less than 41 hours per week? Use a TI-83 Plus/T1-84 Plus calculator. Round the answer to at least four decimal places.

Answer 1

To find the probability that a randomly selected automobile worker works less than 41 hours per week, you can use the standard normal distribution and the z-score formula. Using a TI-83 Plus/T1-84 Plus calculator, the probability is approximately 0.0228 or 2.28%.

Step-by-step explanation:

To find the probability that a randomly selected automobile worker works less than 41 hours per week, we can use the standard normal distribution and the z-score formula.

First, we need to calculate the z-score:

Z = (X - μ) / σ

where X is the value we are interested in (41 hours), μ is the mean (43.6 hours), and σ is the standard deviation (1.3 hours).

Using the formula, we get:

Z = (41 - 43.6) / 1.3 = -1.999

Next, we can use the z-score to find the probability using a standard normal distribution table or a calculator. Using a TI-83 Plus/T1-84 Plus calculator, we can use the normalcdf function:

P(X < 41) = normalcdf(-infinity, -1.999) ≈ 0.0228

Therefore, the probability that a randomly selected automobile worker works less than 41 hours per week is approximately 0.0228 or 2.28%.