Question

QUESTION 9 The probability that a current generation iPhone has a particular flaw is 0.11. A quality control group randomly selects 600 iPhones and checks them for this flaw. Use the Normal Approximation to the Binomial Distribution to estimate the probability that the number of iPhones with the flaw in the sample is at most 56. Round your Z-score to 2 decimal places. Round your answer to 3 decimal places. Do not forget the .5 continuity correction. Hint: The mean is 66 and the standard deviation is 7.66.

Answer 1

Solution:

Given that,

P = 0.11

1 - P = 0.89

n = 600

Here, $X\sim$ BIN ( n , P ) that is , BIN (600 , 0.11)

then,

n*p = 66 > 0.5

n(1- P) = 534 > 5

According to normal approximation binomial,

X $\rightarrow$ Normal

Mean = $\mu$ = n*P = 66

Standard deviation = $\sigma$ =$\sqrt{}$n*p*(1-p) = 7.66

We using continuity correction factor

P( X $\leq$ a ) = P(X < a + 0.5)

P(x < 56.5) = P((x - $\mu$ ) / $\sigma$ < (56.5 - 66) / 7.66)

= P(z < -1.24)

Probability = 0.108