Example: Given below is a company’s future prospect Economic Scenario Profit(RM million) Prob. Great 10 0.2 Good 5 0.4 OK 1 0.25 Bad - 4 0.15 Find the mean and standard deviation of future profit for this company.

Outline of Answer: x p x*p (x-3.65)2 (x-3.65)2 *p 10 0.2 2.0 5 0.4 2.0 1 0.25 0.25 - 4 0.15 -0.6 Sum 3.65 = E(x) V(x) Standard Deviation = Suare root of V(x)

Example: An insurance representative has appointments with 4 prospective clients tomorrow. From the past experience she knows that the probability of making a sale on any appointment is 1 in 5 or 0.20. What is the probability that she will sell a policy to 3 out of 4 prospective clients?

Outline of Answer P(sale)=0.2 P(No sale)=1-0.2=0.8 n=4 P(3 sales)= =0.0256

Example: A company is planning to sell a new product in four areas North, South, East and West. The probability that the product will be successful in an area is 0.3. Success in one area will be independent of success or failure in the other areas. What is the probability of success in no areas, one area, two areas, three areas, and four areas?

Outline of Answer P(success)=p=0.3; q=1-p=0.7; n=4 Use Binomial Tables P(0 successes)=P(0)=0.2401 P(1)=0.4116 P(2)=0.2646 P(3)=0.0756 P(4)=0.0081

Example: Of the total output produced in a factory, 8% is defective Example: Of the total output produced in a factory, 8% is defective. In a batch of 500 units, what is the mean expected number of defective items, and what is the standard deviation?

Outline of Answer N=500; p=0.8 Mean = np = 500*0.8 = 40 units Standard Deviation =

Example: Suppose electric utility bills are based on actual reading of the electric meter and in 1 out of 100 cases, the meter is incorrectly read. What is the expected number of incorrect bills in processing 500 customer bills?

Outline of Answer P(error)=p=0.01 n=500 Mean=λ=np=5

Example: Alden and Associates write weekend trip insurance at a very nominal charge. Records show that the probability that a motorist will have an accident during weekend and file a claim is 0.0005. Suppose Alden wrote 400 policies for the forthcoming weekend. What is the probability that exactly two claims will be filed?

Outline of Answer p=0.0005 n=400 Mean=λ=np=0.2 Using Poisson Tables,

Example: It is thought that, on an average, 0 Example: It is thought that, on an average, 0.01% of the workforce in a particular industry will suffer from an acute form of industrial disease. Hot Flush Sdn.Bhd., employs a workforce of 2,000 men, and the senior medical adviser of the company has stated that if three people in the workforce suffer from the disease, the cases should be treated as a sign that there are unacceptable health hazards. Calculate the probability that three or more men in the workforce will catch the disease.

Outline of Answer p=0.0001 n=2000 Mean=λ=np=0.2 Using Poisson Tables, P(3 or more)=1-P(2 or less) =1-[P(0)+P(1)+P(2)] =1-[0.8187+0.1637+0.0164]=0.0012

Example: A normal distribution has a mean of 100 and a standard deviation of 10. What proportion of total frequencies will be: a) above 100 b) below 100 c) above 50 d) below 75 e) above 80 f) above 85 g) below 108 h) in the range 80 to 110 I) in the range 90 to 95