Question

A survey of 2645 consumers by DDB Needham Worldwide of Chicago for public relations agency Porter/Novelli showed that how a company handles a crisis when at fault is one of the top influences in consumer buying decisions,with 73% claiming it is an influence. Quality of product was the number one influence, with 96% of consumers stating that quality influences their buying decisions. How a company handles complaints was number two, with 85% of consumers reporting it as an influence in their buying decisions. Suppose a random sample of 1,100 consumers is taken and each is asked which of these three factors influence their buying decisions.

a. What is the probability that more than 820 consumers claim that how a company handles a crisis when at fault is an influence in their buying decisions? *

b. What is the probability that fewer than 1,030 consumers claim that quality of product is an influence in their buying decisions? **

c. What is the probability that between 81% and 83% of consumers claim that how a company handles complaints is an influence in their buying decisions? *

*(Round the values of z to 2 decimal places. Round the intermediate values to 4 decimal places. Round your answer to 4 decimal places.) **(Round the values of z to 2 decimal places. Round the intermediate values to 4 decimal places. Round your answer to 5 decimal places.)

Answer 1

Solution:-

a) The probability that more than 820 consumers claim that how a company handles a crisis when at fault is an influence in their buying decisions is 0.9999.

n = 2645

p = 0.73

x = 820

By applying binomial distributiion:-

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

P(x > 820) = 0.9999

b) The probability that fewer than 1,030 consumers claim that quality of product is an influence in their buying decisions is 0.000001.

n = 2645

p = 0.96

x = 1030

By applying binomial distributiion:-

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

P(x < 1030) = 0.000001

c) The probability that between 81% and 83% of consumers claim that how a company handles complaints is an influence in their buying decisions is 0.00199.

p₁ = 0.81

p₂ = 0.83

By applying normal distribution:-

z(p₁ = 0.81) = - 5.76

z(p₂ = 0.83) = - 2.88

P( - 5.76 < z < - 2.88) = P(z > - 5.76) - P(z > - 2.88)

P( - 5.76 < z < - 2.88) = 0.99999 - 0.998

P( - 5.76 < z < - 2.88) = 0.00199