Statistics and Probability Answers

A small company has developed a new product for the electronics industry. The company believes that an advertising campaign costing R2000 would give the product a 70% chance of success. It estimates that a product with this advertising support would provide a return of R11000 if successful and return of R2000 if it not successful. Past experience suggests that without advertising support a new product of this kind would have a 50% chance of success giving a return of R10000 if successful and a return of R1500 if not successful.
Construct a decision tree and write a report advising the company on its best course of action.

A company produces plastic elephants in two colours for the novelty trade market. Production in the factory is on one of three machines; 10% is on machine A, 30% on machine B, and the remainder on machine C. Machine A’s production consists of 40% blue elephants and 60% pink elephants. Machine B’s production consists of 30% blue elephants and 70% pink elephants. Machine C’s production has 80% pink elephants with the remainder being blue.
2.1.1 What proportion do blue elephants form of total production? (5)
2.1.2 If a particular elephant is pink, what is the probability it was made by machine B?

A marketing manager makes the statement that the long-run probability that a
customer would prefer the deluxe model to the standard model is 30%.
1.2.1 What is the probability that exactly 3 in a random sample of 10 customers will
prefer the deluxe model? (3)
1.2.2 What is the probability that more than 2 in a random sample of 10 customers
will refer the standard model?

The desired percentage of silicon dioxide in a certain type of cement is 5. A random sample of 36 specimens gave a sample average percentage of 5.21 and a sample standard deviation of 0.38. Use a significance level of 0.01 and test whether the sample result indicates a change in the average percentage.

1.1 The records of 400 examinees are given below:
Score
Educational Qualification
Total
Diploma
Degree
I.T
Below 50
90
30
60
180
Between 50 and 60
20
70
70
160
Above 60
10
30
20
60
Total
120
130
150
400
If an examinee is selected at random from this group, find:
1.1.1 The probability that he is a Diploma graduate. (3)
1.1.2 The probability that he is a Degree graduate, given that his scores are above
60. (3)
1.1.3 The probability that his score is below 50, given that he’s doing IT. (3)

A town-planning sub-committee in Tshwane wanted to know if there is any difference in the mean travelling time to work of car and Train commuters. They there carried out a survey amongst car and bus commuters and with the following sample statistics:
Car Commuters
Train Commuters
X1= 29.6 min
X2 = 25.2 min
S1= 5.2 min
S2= 2.8 min
N1=22 drivers
N2=36 passengers
4.1 Test the hypothesis at the 5% significance level that it takes car commuters to get to work earlier than Train commuters.

60% of invoices arw paid within 10 days.
17 invoices are randomly selected. What is the probability that 16 of the invoices randomly chosen will be paid in 10 days?

Consider a random variable X such that P(x=1)=1/4 and P(x=0)=3/4. E(x)=1/4 and standard deviation is sqrt(3)/4. If X1, X2,..., Xn is a random sample of the population X, then lim n -> infinity of P(X1+X2+...+Xn/n > C) = 0 for every C>1/4.

It is not known whether a coin is fair or infair. If the coin is fair, the probability of a tail is 0.5, bt if the coin is unfair, the probability of a tail is 0.1. If the probability of a fair coin is 0.8 and the probability of a unfair coin is 0.2, the coin is tossed once, and a tail is the result: 1. What is the probability that the coin is fair. 2. What is the probability that the coin is infair.

Assume that the samples are independent and that they have been randomly selected. Construct a 90% confidence interval for the difference between population proportions p1-p2. Round to three decimal places.

x1=24, n1=51, x2=29, n2=56