A die is tossed 180 times. Find the expected number `(mu)` of times the face
with the number 5 will appear. Also find the standard deviation `(sigma)` and variance `(sigma^(2))`

Explanation

In a single throw of a die `S={1,2,3,4,5,6}`
p= (probability of getting the number ) `=(1)/(6)`
`:. , q =(1-p)=(1-(1)/(6))=(5)/(6)`
Thus n=180 `p=(1)/(6) " and " q=(5)/(6)`
`:. Mu =np =(180 xx (1)/(6) ) =30`
Variance `=sigma^(2) = npq =(180 xx (1)/(6) xx(5)/(6)) =25`
Standard deviation `=sigma =sqrt(25)=5`