Question

Question 7 (1 mark) Attempt 1 Each hour an operator inspects 100 pencils and determines if they are acceptable. Historically the proportion of unacceptable pencils has been 0.01 Find the probability that there are between 1 and 3, inclusive, unacceptable pencils Use the Normal approximation to the Binomial distribution. Your answer can be rounded to three decimal digit accuracy when entered Probability isSkipped

Answer 1

Solution:

n = 100

p = 0.01

binomial probability distribution

Formula:

P_{(k out of n )}= n!*p^k * q^n-k / k! *(n - k)!

P( 1 $\leq$ x $\leq$ 3 ) = 100!*0.01¹ * 0.99^100-1 / 1! *(100 - 1)!+100!*0.01² * 0.99^100-2 / 2! *(100 - 2)!

+100!*0.01³ * 0.99^100-3 / 3! *(100 - 3)!

= 0.3697+0.1849+0.0610

= 0.6156