Question

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 1

P( x < 8) = 0.0344

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 =
`√(n p q) = √(20 X 0.60 X 0. 40) = 2.19`

Standard deviation σ = 2.19

Step(ii):-

Let 'X' be the random variable of normal distribution

Let 'x' = 8

`Z = (x-mean)/(S.D) = (8-12)/(2.2) = -1.82`

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