Kindly Show the Calculation Typed or on Excel Megastat Q.4) A man claims to be a
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Question
Kindly Show the Calculation Typed or on Excel Megastat
Q.4) A man claims to be able to distinguish between two kinds of wine with 90% accuracy and presents his claim to an agency interesting in promoting one of the wines. The following experiment is proposed to check his claim:
The man is to taste the two types of wine and distinguish between them. This is to be done nine times with a three-minute break after each taste.
It is agreed that if the man is correct at least six out of the nine times, he will be hired.
The main questions to be asked are:
On the one hand, does the above procedure give sufficient protection to a person who is just guessing?
On the other hand, is the man really given a sufficient chance to be hired if he really is a wine connoisseur?
Explanation / Answer
let X be the number of times a man can distinguish between the two types of wine out of 9 times.
let p be the probability of successfully distinguishing between two types of wine.
hence X~Bin(9,p)
hence the pmf of X is P[X=x]=9Cxpx(1-p)9-x x=0,1,2,3,...,9
if the man is correct at least six out of the nine times, he will be hired.
a) for a man who is just guessing p=0.5
hence X~Bin(9,0.5) so P[X=x]=9Cx(0.5)9
so P[X>=6]=P[X=6]+P[X=7]+P[X=8]+P[X=9]
=9C6(0.5)9+9C7(0.5)9+9C8(0.5)9+9C9(0.5)9
=0.59[84+36+9+1]=0.2539
which is quite low. his chance of being hired is only 25.39%
hence the above procedure does not give sufficient protection to a person who is just guessing. [answer]
b) if he really is a wine connoisseur then p=90%=0.9
hence X~Bin(9,0.9) so P[X=x]=9Cx(0.9)x(0.1)9-x
so P[X>=6]=P[X=6]+P[X=7]+P[X=8]+P[X=9]
=9C6(0.9)6(0.1)9-6+9C7(0.9)7(0.1)9-7+9C8(0.9)8(0.1)9-8+9C9(0.9)9(0.1)9-9
=84(0.9)6(0.1)3+36(0.9)7(0.1)2+9(0.9)8(0.1)+(0.9)9
=0.9916689
hence his chance of being hired is 99.16689%
hence the man is given sufficient chance to be hired if he really is a wine connoisseur [answer]
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