Please, can you help in this question. I need to help just in letter c and d - I already did letter a and b.

3) The acidity of soils is measured by pH, which may range from 0 (high acidity) to 14 (high alkalinity). A soil scientist wants to estimate the average pH for a large field by randomly selecting n = 40 samples.

a) Suppose = 0.75. Find the probability that the sample mean of the 40 pH measurements will be within 0.2 unit of the true mean pH of the field. b. Refer to question

b) Suppose the scientist would like the sample mean to be within 0.1 of the true mean with probability 90%. How many sample should the scientist take?

c) When two independent large samples are selected, the difference in the sample means