A fair die is to be rolled 20 times. Find the expected value and standard deviation of the # of times? (a) 6 appears b) 5 or 6 appears.?

a)

n=20

p=1/6 (probability of rolling 6)

Expected vaalue = np = 20*1/6 = 3.33

Standard deviation = sqrt(np(1-p)) = sqrt((20)(1/6)(5/6)) = 1.6667

P(5 or 6) = 2/6=1/3

p= probability of rolling 5 or 6 = 2/6= 1/3

Expected vaalue = np = 20*1/3 = 6.67

Standard deviation = sqrt(np(1-p)) = sqrt((20)(1/3)(2/3)) = 2.108

a) P(rolling a 6) = p = 1/6

n = 20

E(X) = np = 20*1/6 = 3.33

SD = sqrt [n*p*(1-p)]

= sqrt [20*1/6*(1-1/6)]

= sqrt [20*1/6*5/6]

= 1.67

b) P(rolling a 5 or 6) = 2/6 or 1/3

n = 20

E(X) = 20*1/3 = 6.67

SD = sqrt [20*1/3*(1-1/3)]

= 2.11