Reference no: EM132845033
a) The number of chocolate chips in an 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips.
i. What is the probability that a randomly selected bag contains between 1000 and 1400 chocolate chips?
ii. What is the probability that a randomly selected bag contains fewer than 1025 chocolate chips?
iii. What proportion of bags contains more than 1200 chocolate chips?
iv. What is the percentile rank of a bag that contains 1050 chocolate chips?
b) Steel rods are manufactured with a mean length of 23 centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.06 cm.
i. What proportion of rods has a length less than 22.9 cm?
ii. Any rods that are shorter than 22.85 cm or longer than 23.15 cm are discarded. What proportion of rods will be discarded?
iii. Using the results of part (b), if 5000 rods are manufactured in a day, how many should the plant manager expect to discard?
iv. If an order comes in for 10,000 steel rods, how many rods should the plant manager expect to manufacture if the order states that all rods must be between 22.9 cm and 23.1 cm?
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