Suppose that the weight in kilograms of a person randomly selected from a population

is a random variable X with a normal distribution with parameters μ and [tex]\sigma^2[/tex].Also suppose that [tex]P(X\leq 60) =1/2[/tex] and [tex]P(X\leq 52) = 1/4[/tex].

a) Find the value of the parameters μ and σ.

b) Find [tex]P(X \leq 75)[/tex]

c) At least how many standard deviations away from μ must X be for the probability to be greater than or equal to 0.95? That is, find k such that [tex]P(|X-\mu | \ \textless \ k \sigma)\geq 0.95[/tex]