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][tex]P(|X- \mu| \ \textless \ k \sigma) \geq 0.95[/tex]^{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 \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