please answer, show all your work and draw line graph foe each question.

Lower reading = 1.9168 (#15-16) Entomologist Heinz Kaefer has a colony of bongo spiders in his lab. Assume their weights are normally distributed with a mean of 11 grams and standard deviation of 2 grams. 15. About what percent of spiders in the colony weigh between 7 grams and 13 grams? 16. What z-score corresponds to a spider in this colony that weighs 12 grams? 17. Your lumber company has bought a machine that automatically cuts lumber. The seller of the machine claims the machine cuts lumber to a mean length of 8 feet (96 inches) with standard deviation of 0.5 inches. Assume the lengths are normally distributed. You randomly select 40 boards and find the mean length is 96.25 inches. What is the probability the mean of the sample is 96.25 inches or more? 18. A manufacturer claims the mean weight of its ice-cream cartons is 10 ounces with standard deviation of 0.5 ounces. Assume the weights are normally distributed. You randomly select 25 cartons and find their mean weight is 10.15 ounces. What is the probability the mean of the sample is less than 10.25 ounces