Question

Suppose you are investigating whether there is a difference in taste between organic milk and regular milk. You recruit 16 random volunteers and ask each one individually after tasting to tell you which of two unmarked glasses contains the organic milk. Let X be the number of correct guesses. If there really were no difference in taste between organic milk and regular milk, what would be the probability of exactly six correct guesses, to three decimal points?

Answer 1

SOLUTION:

FROM GIVEN DATA,

Suppose you are investigating whether there is a difference in taste between organic milk and regular milk. You recruit 16 random volunteers and ask each one individually after tasting to tell you which of two unmarked glasses contains the organic milk. Let X be the number of correct guesses. If there really were no difference in taste between organic milk and regular milk, what would be the probability of exactly six correct guesses, to three decimal points

Here as there is no difference probability of right guess = 0.5

Hence for binomial distribution parameter p = 0.5

n = 16

Hence probability of exactly six correct guesses =

{ calculation for ... it is in the form of  ⁿC_r = n! / (r! * (n-r) !) where n = 16 and r = 6 by substitution the value we get 16! / (6! * (16-6)!) = 16! / (6! * 10!) = (16*15*14*13*12*11*10!) / (6! * 10!) = (16*15*14*13*12*11) / (6*5*4*3*2*1)  

= 4*14*13*11 = 8008}

= 8008 *0.015625 *0.0009765625

= 0.12219

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