It is estimated that 17% of the vehicles entering Canada from the United States carry undeclared goods. Use the normal approximation to calculate the probability that a search of 900 randomly selected vehicles will find more than 175 with undeclared goods.

The probability that a search of 900 randomly selected vehicles will find more than 175 with undeclared goods.

P( x > 175) = 0.0256

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 900

The estimated proportion 'p' = 0.17

Mean of the binomial distribution

                       μ = n p = 900 × 0.17 = 153

Standard deviation of the binomial distribution

                     σ =

Step(ii):-

Let 'X' be the random variable of normal distribution

mean  μ= 153 and σ = 11.26

Given X = 175

The probability that a search of 900 randomly selected vehicles will find more than 175 with undeclared goods.

P( x > 175) = P( Z> 1.95)

                = 1- P( Z < 1.95)

                =   1  - ( 0.5 +A( 1.95))

               =   0.5 - A( 1.95)

              =   0.5 - 0.4744

              = 0.0256

Conclusion:-

The probability that a search of 900 randomly selected vehicles will find more than 175 with undeclared goods.

P( x > 175) = 0.0256

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