Reference no: EM132385367

Assignment

A sale satisfaction survey in 2005 asked consumers whether they agreed with the statement "The car safety is the most important feature."

The responses classified by age, gender, and response. Data can be found in the Excel file AS2.XLSX (survey) in the Excel directory. [20]

In part a, b, c, and d, if you randomly select a person from this sample what is the probability that:

1. The person supports (agreed) the statement?

2. The person is younger than fifty years old?

3. The person agrees with the statement and he/she is younger than fifty years old?

4. The person agrees with the statement and is younger than fifty years old?

5. A person who responded disagree is a male?

6. If you select a person who is a male, what is the probability he responded neither agree nor disagree?

7. If you select a person who is a female, what is the probability she responded disagree or agree?

8. Are response and gender independent events?

2. A recent survey regarding online shopping shows customers' purchase when instant discount, free shipping, or no special offer were given. The probability of the purchase is 8%, 6.5%, and 1.5% respectively. A sale manager offers free shipping option to 30% and an instant discount to 20% of the customers.

a) Construct a probability tree for this experiment.

b) What percent of customers who visit site did not make a purchase?

c) If a customer makes a purchase, what is the probability that he/she had a offer of free shipping?

The sale manager also emailed three coupons, gold, silver, and green, to the equal numbers of customers to see which one would lead to the highest probability of purchase. Three months sale data shows increased probability of purchases; 2.5% for gold, 4.1% for silver, and 3.7% for green coupons.

4. d)  Construct a probability tree for this experiment.

5. e)  What percent of customers who visited the site did make a purchase?

6. f)  What is the probability that a randomly selected customer has a silver coupon?

3. An insurance company divided its clients into two categories, amateur and professional. The last year accident report shows 10% of amateur drivers and 2.5% of professional drivers are involved in an accident. If 15% of drivers are amateur license and 85% are professional, find the following probabilities. For simplicity, assume year to year accident accidents for any driver are independent. [20]

1. a)  What is the probability of accident for a driver?

2. b)  What is the probability that an amateur driver is involved in at least one accident during 3 years?

3. c)  What is the probability of not having an accident for a professional driver during 3 years?

4. d)  The annual insurance premium is computed according to being involved to at least one accident in 3 years. If a professional driver pay $1000 premium, how much the premium of amateur drivers should be?

4. The daily demand for small vegetarian pizza at a local store is normally distributed with mean of 122 and a standard deviation of 15 pizza.

1. a)  What is the probability that the store has less than 86 orders in a day?

2. b)  What is the probability that number of orders is between 85 and 112?

3. c)  The store is planning for a long weekend. What is a probability that it can sell over 140 pizza?

4. d)  How many pizzas should the store sell to ensure that it runs short on no more than 20% of days?

5. According to a university research report, 58% of graduate students believe saving energy should be given priority for developed countries.

Suppose that a professor randomly selects 18 students and ask their opinion.

1. a)  What is the probability that exactly 14 students vote in favour of saving energy?

2. b)  What is the probability that 6 students and more vote in favour of saving energy?

3. c)  What is the probability that less than 9 students vote in favour of saving energy?

Attachment:- sale-survey.rar