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Estimate the indicated probability by using the normal distrtbution as an approximation to the binomial distribution
19) With n=20 and p = 0,60, estimate P(fewer than 8).

Answer :

Answer:

P( x < 8) = 0.0344

Step-by-step explanation:

Step(i):-

Given 'n' = 20 and 'p' = 0.60

Mean of the binomial distribution = n p

μ = n p = 20 × 0.60 = 12

Mean 'μ' = 12

Standard deviation of the binomial distribution = [tex]\sqrt{n p q} = \sqrt{20 X 0.60 X 0. 40} = 2.19[/tex]

Standard deviation σ = 2.19

Step(ii):-

Let 'X' be the random variable of normal distribution

Let 'x' = 8

[tex]Z = \frac{x-mean}{S.D} = \frac{8-12}{2.2} = -1.82[/tex]

P( x < 8) = P( Z< -1.82)

            = 1- P( Z>1.82)   (∵ A(-1.82) = A(1.82)

           = 1 - (0.5 + A( 1.82))

          = 0.5 - A (1.82)

         = 0.5 - 0.4656

        = 0.0344

Conclusion:-

P( x < 8) = 0.0344

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