If X is N5 16 find a constant c such that Px5 c 08413Soluti

If X is N(5, 16), find a constant c such that P(|x-5|? c) = 0.8413.

Solution

X is a normal variate with mean 5 and std dev = 16.

Hence from std normal distribution table we get z value for

P (Z<=z) = 0.8413 as 1.00

Hence |x-5|<=sigma = 16 is 0.8413

Simplify to get

-11<=x<=21