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If Mrs. fields herself wants to verify that rate by beginning with a small sample of 10 randomly selected consumers, find the probability that exactly 9 of the 10 consumers recognize her brand name. Also, find the probability that the number who recognize her brand name is not nine.

Sagot :

Cricetus

Answer:

The correct approach will be "0.612580".

Step-by-step explanation:

Given:

Randomly selected customers,

n = 10

Probability of recognition,

p = 90%

or,

  = 0.9

q = 1 - p

  = 1 - 0.9

  = 0.1

Now,

The probability that 9 out of 10 clients are likely to be familiar with the brand will be:

⇒ [tex]P(X=r)=nCr\times (p)^r\times (q)^{(n-r)}[/tex]

⇒ [tex]P(X=9)=10C_9\times (0.9)^9\times (0.1)^{(10-9)}[/tex]

                    [tex]=10C_9\times (0.9)^9\times (0.1)^1[/tex]

                    [tex]=10\times (0.9)^9\times 0.1[/tex]

                    [tex]=0.387420[/tex]

hence,

The probability that not nine seem to be the numbers recognizing her brand name will be:

⇒ [tex]P(X=not \ 9)=1-P(X=9)[/tex]

                          [tex]=1-0.387420[/tex]

                          [tex]=0.612580[/tex]

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