Final answer:
The correct option is d) 0.500. A machine makes parts that weigh an average of 3 kg with a standard deviation of 480 g. We consider two batches of 920 pieces each. To find the probability that the weight difference between the two batches is greater than 4.5 kg, we need to calculate the z-score and then find the corresponding probability.
Step-by-step explanation:
Problem:
A machine makes parts that weigh an average of 3 kg with a standard deviation of 480 g. We consider two batches of 920 pieces each. Describe completely this situation, define all the data, and explain the method, and all steps of computation.
Solution:
Given data:
Mean weight of the parts (μ) = 3 kg
Standard deviation (σ) = 480 g
To find the probability that the weight difference between the two batches is greater than 4.5 kg, we need to calculate the z-score and then find the corresponding probability.
The formula for calculating the z-score is:
z = (x - μ) / σ
First, convert the weight difference of 4.5 kg to grams, since the standard deviation is given in grams:
Weight difference (x) = 4.5 kg * 1000 g/kg = 4500 g
Next, calculate the z-score:
z = (4500 - 0) / 480 = 9.375
To find the probability corresponding to a z-score of 9.375, consult the z-table or use a calculator. The probability will be close to 1, which means it is certain that the weight difference between the two batches is greater than 4.5 kg.
Therefore, the correct option is d) 0.500.