Plastic pollution of waters is a dramatic issue for the fauna and potentially/eventually, for humans... Assume that in a given body of water, plastic concentration per liter follows a normal distribution with a population mean of 500 units and a population variance of 625 units 2. In the conditions above,

a.1) What is the probability that in a 1-liter sample of that water, plastic concentration exceeds 487.5 units?

a.2) What is the probability that in a 1-liter sample of that water, plastic concentration varies from 462.5 to 512.5 units?

b) Plastic concentration has been measured for each of 25 1-liter samples taken from the body of water considered above. In other words, an i.i.d. random sample of size 25 is collected from a normal distribution of plastic concentration with the parameter values given on the previous page. Calculate the probability that the sample mean differs from the population mean by more than 5 units.

c) What is the minimum value of n (sample size) for the sample mean of plastic concentration in the same body of water to be smaller than 505 units with a probability of 0.8?