Question

PLEASE SHOW AND EXPLAIN ALL WORK.

Records have shown that historically 15% of consumers are unhappy with a new product. A poll of 200

consumers is to be conducted regarding a recently released product. What is the probability that more

than or equal to 40 consumers will be unhappy with the product?

Answer 1

sample size is n = 200 and probability p = 0.15

Using binomial to normal approximation

n*p = 200*0.15= 30

and

n(1-p) = 200*(1-0.15) = 170

Both are greater than 5, we can use the normal approximation.

mean = n*p = 200*0.15 = 30

and standard deviation = sqrt{n*p*q}

where n = 200, p = 0.15 and q=1-p= 1-0.15 = 0.85

this implies

standard deviation =

To find:- Probability of more than or equal to 40 consumers will be unhappy

where a = 40

this implies

Using z distribution table for z value 1.88

we get

{check first left column for 1.8 and first row for 0.08, then select the intersecting cell}

Required probability is 0.0301