Step 1 :First, we need to calculate the z-scores for 1000 and 1500. The mean (μ) is 1252 and the standard deviation (σ) is 129. The formula for a z-score is \( (X - μ) / σ \). So, the z-score for 1000 is \( (1000 - 1252) / 129 \) and the z-score for 1500 is \( (1500 - 1252) / 129 \).
Step 2 :Then, we need to find the probabilities associated with these z-scores. The probability of a bag containing between 1000 and 1500 chips is the difference between the probabilities of the bag containing less than 1500 chips and the bag containing less than 1000 chips.
Step 3 :Let's calculate these values. The z-score for 1000 is -1.9534883720930232 and the z-score for 1500 is 1.9224806201550388. The probability for 1000 is 0.025380876893736335 and the probability for 1500 is 0.9727273450797767.
Step 4 :The probability of a bag containing between 1000 and 1500 chips is the difference between the probabilities of the bag containing less than 1500 chips and the bag containing less than 1000 chips, which is \( 0.9727273450797767 - 0.025380876893736335 = 0.9473464681860403 \).
Step 5 :The probability that a randomly selected bag contains between 1000 and 1500 chocolate chips is approximately 0.9473, or 94.73%. This means that about 94.73% of bags will contain between 1000 and 1500 chips.
Step 6 :Final Answer: The probability that a randomly selected bag contains between 1000 and 1500 chocolate chips is \( \boxed{0.9473} \).