The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with a mean of 1252 chips and standard deviation 129 chips. (a) What is the probability that a randomly selected bag contains between 1000 and 1400 chocolate chips, inclusive? (b) What is the probability that a randomly selected bag contains fewer than 1100 chocolate chips? (c) What proportion of bags contains more than 1225 chocolate chips? (d) What is the percentile rank of a bag that contains 1475 chocolate chips? (a) The probability that a randomly selected bag contains between 1000 and 1400 chocolate chips, inclusive, is (Round to four decimal places as needed.) (b) The probability that a randomly selected bag contains fewer than 1100 chocolate chips is (Round to four decimal places as needed.) (c) The proportion of bags that contains more than 1225 chocolate chips is (Round to four decimal places as needed.) (d) A bag that contains 1475 chocolate chips is in the th percentile. (Round to the nearest integer as needed.)

Step 1 ：We are given a normal distribution with a mean of 1252 and a standard deviation of 129. We are asked to find the probability of certain events occurring within this distribution.

Step 2 ：For part (a), we need to find the probability that a randomly selected bag contains between 1000 and 1400 chocolate chips. This is equivalent to finding the probability that a random variable from this distribution is less than or equal to 1400 and subtracting the probability that it is less than or equal to 1000. The probability is approximately 0.8490.

Step 3 ：For part (b), we need to find the probability that a randomly selected bag contains fewer than 1100 chocolate chips. This is equivalent to finding the probability that a random variable from this distribution is less than or equal to 1100. The probability is approximately 0.1193.

Step 4 ：For part (c), we need to find the proportion of bags that contains more than 1225 chocolate chips. This is equivalent to finding the probability that a random variable from this distribution is greater than 1225, which is 1 minus the probability that it is less than or equal to 1225. The proportion is approximately 0.5829.

Step 5 ：For part (d), we need to find the percentile rank of a bag that contains 1475 chocolate chips. This is equivalent to finding the percentile of 1475. The percentile rank is approximately 96.

Step 6 ：Final Answer: (a) The probability that a randomly selected bag contains between 1000 and 1400 chocolate chips, inclusive, is approximately \(\boxed{0.8490}\). (b) The probability that a randomly selected bag contains fewer than 1100 chocolate chips is approximately \(\boxed{0.1193}\). (c) The proportion of bags that contains more than 1225 chocolate chips is approximately \(\boxed{0.5829}\). (d) A bag that contains 1475 chocolate chips is in the \(\boxed{96}\)th percentile.