Question

The probability that a current generation iPhone has a particular flaw is 0.07. A quality control group randomly selects 900 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 59. 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 63 and the standard deviation is 7.65.

Answer 1

Solution :

Given that,

p = 0.07

q = 1 - p =1-0.07=0.93

n = 900

Using binomial distribution,

Mean = = n * p = 900*0.07=63

Standard deviation = = n * p * q =   900*0.07*0.93=7.65

Using continuity correction ,

P(x 59) = P((x - ) / < (59-63) /7.65 )

= P(z <-0.52 )

Using z table

Probability = 0.3015