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).

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 =

Standard deviation σ = 2.19

Step(ii):-

Let 'X' be the random variable of normal distribution

Let 'x' = 8

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

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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