e) Statistical Inferences are:
- Average annual income of Bloomberg Businessweek North American subscriber
- Proportion of having an American Express credit card
Question 4:
Motorola used the normal distribution to determine the probability of defects and the
number of defects expected in a production process. Assume a production process
produces items with a mean weight of 10 ounces. Calculate the probability of a defect
and the expected number of defects for a 1000-unit production run in the following
situations.
a. The process standard deviation is .15, and the process control is set at plus or minus
one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces
will be classified as defects.
b. Through process design improvements, the process standard deviation can be reduced
to .05. Assume the process control remains the same, with weights less than 9.85 or
greater than 10.15 ounces being classified as defects.
c. what is the advantage of reducing process variation, thereby causing process control
limits to be at a greater number of standard deviations from the mean?
Set X is weights per unit =>X ~ N(muy=10; xichma^2)
The probability of a defect = 0,1587 + 0,1587= 0,3174
The expected number of defects for a 1000-unit production is = 0,3174 x 1000 = 317,4
Question 3:
A large consumer goods company ran a television advertisement for one of its soap
products. On the basis of a survey that was conducted, probabilities were assigned to the
following events.
B = individual purchased the product
S = individual recalls seeing the advertisement
B ∩ S = individual purchased the product and recalls seeing the advertisement
The probabilities assigned were P(B) = .20, P(S) = .40, and P(B ∩ S) = .12.
a. What is the probability of an individual’s purchasing the product given that the
individual recalls seeing the advertisement? Does seeing the advertisement increase the
probability that the individual will purchase the product? As a decision maker,
would you recommend continuing the advertisement (assuming that the cost is
reasonable)?
b. Assume that individuals who do not purchase the company’s soap product buy from its
competitors. What would be your estimate of the company’s market share? Would you
expect that continuing the advertisement will increase the company’s market share?
Why or why not?
Estimate of the company’s market share = P(B) = 0,2 = 20%
Estimate of the competitors’s share = P(Bngang) = 0,8 = 80%
c. The company also tested another advertisement and assigned it values of P(S) = .30
and P(B ∩ S) = .10. What is P(B ∣ S) for this other advertisement? Which advertisement
seems to have had the bigger effect on customer purchases?