Height classes 120–130,130–140,140–150,150–160,160–170 cm have frequencies \(12,18,p,15,5\). Conditions in
and
are independent.
Find the greatest \(p\) for which the middle observation, or both middle observations when the total is even, lies or lie in the 130–140 class.
Find the greatest \(p\) for which 150–160 is the unique modal class.
Given that there are 60 students, find \(p\), draw the histogram, estimate the mean, and find \(P(h<150)\), \(P(h<130\text{ or}\hspace{0.5em}h\ge160)\), \(P(h>170)\).