1. A study used the 2018-2019 National Health and Nutrition Examination Survey (NHANES) to estimate dietary intake of 6 key nutrients. One of those nutrients was calcium (mg). They found in all adults 65 years or older a mean daily calcium intake of 650 mg with a standard deviation of 420. Using these values for the mean and standard deviation for the U.S. population, find the probability that a random sample of size 75 will have a mean of:

a. Greater than 800 mg. Show your work.

b. Less than 700 mg. Show your work.

c. Between 675 and 720 mg. Show your work.

d. Between 590 and 620 mg. Show your work.

e. Greater than 750 or less than 600 mg. Show your work.