The salinity, or salt content, in the ocean is expressed in parts per thousand (ppt). The number varies with depth, rainfall, evaporation, river runoff, and ice formation. The mean salinity of the oceans is 35 ppt.9 Suppose the distribution of salinity is normal and the standard deviation is 0.52 ppt, and suppose a random sample of ocean water from a region in the tropical Pacific Ocean is obtained.
a. What is the probability that the salinity is more than 36 ppt?
b. What is the probability that the salinity is less than 33.5 ppt?
c. A certain species of fish can only survive if the salinity is between 33 and 35 ppt. What is the probability that this species can survive in a randomly selected area?
d. Find a symmetric interval about the mean salinity such that 50% of all salinity levels lie in this interval. What are the endpoints of this interval called?
Many people grab a granola bar for breakfast or for a snack to make it through the afternoon slump at work. A Kashi GoLean Crisp Chocolate Caramel bar is 45 grams, and the mean amount of protein in each bar is 8 grams.10 Suppose the distribution of protein in a bar is normally distributed and the standard deviation is 0.15 gram, and a random Kashi bar is selected.
a. What is the probability that the amount of protein is less than 7.75 grams?
b. What is the probability that the amount of protein is between 7.8 and 8.2 grams?
c. Suppose the amount of protein is at least 8.1 grams. What is the probability that it is more than 8.3 grams?
d. Suppose three bars are selected at random. What is the probability that all three will be between 7.7 and 8.3 grams?