Answer to Question #123144 in Statistics and Probability for Neetu

Question

Find the lowest height among the tallest 5 students in a class with given mean 165cm and SD of the normal distribution is 25 cm.

Answer 1

Let it be 60 students in a class, so 5 tallest students is 5/60=8.3% in a class;

P(x>X)=1-P(x<X)=0.083,

P(x<X)=1-0.083=0.917, using table, z-value for it equals 1.39.

(X-μ)/σ =1.39,

(x-165)/25=1.39,

x=165+25*1.39=199.75.

So, the lowest height among the tallest 5 students in a class equals 200cm.