1) If n = 5 and (pi) = 0.40, a) P(X) = 4 = 0.0768 b) P(X) 3 = 0.9130 c) P(X) < 2
ID: 3377345 • Letter: 1
Question
1) If n = 5 and (pi) = 0.40,
a) P(X) = 4 = 0.0768
b) P(X) 3 = 0.9130
c) P(X) < 2 = 0.3370
With 15 observations,
a) the smallest of the standard normal quartile values covers an area under the normal curve of ___ /16 = ____ . The corresponding Z-value is -1.53.
b) The largest of the standard normal quantile values covers an area under the normal curve of ___ /16 = ____ . The corresponding Z-value is +1.53.
c) The middle of the standard quantile values covers an area under the normal curve of ___ /16 = _____ . The corresponding Z-value is 0.00.
Explanation / Answer
Binomial Distribution
PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
P( X = 4 ) = ( 5 4 ) * ( 0.4^4) * ( 1 - 0.4 )^1
= 0.0768
P( X < = 3) = P(X=3) + P(X=2) + P(X=1) + P(X=0)
= ( 5 3 ) * 0.4^3 * ( 1- 0.4 ) ^2 + ( 5 2 ) * 0.4^2 * ( 1- 0.4 ) ^3 + ( 5 1 ) * 0.4^1 * ( 1- 0.4 ) ^4 + ( 5 0 ) * 0.4^0 * ( 1- 0.4 ) ^5
= 0.913
P( X < 2) = P(X=1) + P(X=0)
= ( 5 1 ) * 0.4^1 * ( 1- 0.4 ) ^4 + ( 5 0 ) * 0.4^0 * ( 1- 0.4 ) ^5 +
= 0.337
Note: Post the remaining parts in diffrent threadd
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