A coin was flipped 12 times and came up heads 10 times A Cal

A coin was flipped 12 times and came up heads 10 times.

A. Calculate a p-value for the observed sample outcome, using the normal distribution. (Take all intermediate calculations to at least 3 decimal places. Round your z-value to 2 decimal places. Round your answer to 4 decimal places.)

Solution

A.
Proportion ( P ) = 10/12 = 0.8333
Standard Deviation ( sd )= Sqrt (P*Q /n) = Sqrt(0.8333*0.1667/12) =
Normal Distribution = Z= X- u / sd ~ N(0,1)                  

B.
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 = 10 ) = ( 12 10 ) * ( 0.5^10) * ( 1 - 0.5 )^2
= 0.0161

P( X = 11 ) = ( 12 11 ) * ( 0.5^11) * ( 1 - 0.5 )^1
= 0.0029

P( X = 12 ) = ( 12 12 ) * ( 0.5^12) * ( 1 - 0.5 )^0
= 0.0002

P( X > = 10 ) = P( X = 10 ) + P( X = 11 ) + P( X = 12 ) = 0.0193