Analysis of Descriptive Statistics, Probability Distributions Assignment

Assignment Task

Question

1. For a particular type of life insurance policy, the lifetimes of the policy holders are known to follow normal distribution with mean = 67.2 years and standard deviation of 4.8 years. The policy stipulates a payment following the 65^th birthday and a payment every 5 years after that.

1. What percentage of policy holders will receive no payment under the policy?

2. What percentage of policy holders will receive two or more payments under this policy?

3. What percentage of policy holders will exactly three payments under the policy?

2. The average monthly sales of ‘Sundaram ‘computers are 2600 units with a standard deviation of 110 units. The sales are found to be normally distributed over months

• Determine the probability that the sales during a particular month will be at least 2400.
• A new monthly sales target is to be set which at present corresponds to top 15% of sales. What should the new sales target be?
• Determine the probability that the sales during a particular month will be between 2555 and 3150.
• What should the new sales target for 45% of the sales?

3.  According to a report by AC-Neilson, the average monthly household cellular phone bill is Rs.3000. Suppose local monthly household cell phone bills are normally distributed with a standard deviation of Rs. 550.

1. What is the proportion that a randomly selected monthly cell phone bill is more than Rs.4250?

2. What is the proportion that a randomly selected monthly cell phone bill is between Rs.2250 and Rs.3500?

3. What is the proportion that a randomly selected monthly cell phone bill is between Rs.3250 and Rs.3750?

4. What is the proportion that a randomly selected monthly cell phone bill is no more than Rs.2000?

5. What is the required monthly cell phone bill for the top 30% of the households?

4. The National Bank has found that the average daily balance in its customer’s savings accounts is Rs. 8000 with a standard deviation of Rs. 2000. Further the average daily balances have been found to be normally distributed

1. What % of bank savings account holders carries average daily balances in excess of Rs. 11000?
2. What % of bank savings account holders carries average daily balances between 6500 and Rs. 10500?
3. What % of bank savings account holders carries average daily balances in excess of Rs. 11000?
4. The bank is considering issuing free drafts up to Rs. 10000 to customers carrying average daily balances in excess of a certain amount. If the bank does not want to give this facility to more than 5% of its customers, what minimum average daily balance should it prescribe?

5. The U.S. Bureau of Economic Statistics reports that the average annual salary in the metropolitan Boston area is $50542. Suppose annual salaries in the metropolitan Boston area are normally distributed with a standard deviation of $4246. A Boston worker is randomly selected.

1. What is the probability that the worker’s annual salary is more than $ 60000?

2. What is the probability that the worker’s annual salary is less than $ 45000?

3. What is the probability that the worker’s annual salary is between $44000 and $52000?

4. What is the least salary offered to 60% of worker’s?

5. What is the salary offered to top 15% of workers?

6. In a survey with a sample of 200 private clinics, the daily number of patients treated follows a normal distribution with its mean and standard deviation as 85 and 20 respectively

• What is the probability that the daily number of patients treated is less than 80? Also find the number of clinics having the daily number of patients treated less than 80.

• What is the probability that the daily number of patients treated is more than 60? Also find the number of clinics having the daily number of patients treated more than 60.

• How many patients are expected to arrive if the clinic operates with 75% of its capacity

• What is the probability that the daily number of patients treated is between 65 and 85?. Also find the number of clinics having the daily number of patients treated more than 65.

7. All insurance companies offering unit linked insurance policies, charge certain amount of money by way of meeting initial expenses. However, the percentages of such expense ratio vary from company to company. The following table gives the expense ratio including allocation charges for some companies and some maturity period.

Comment on the comparative assessment of insurance policies based on Descriptive Statistics

8. Star Bazaar has recorded the following sales ( in ‘000 from four departments in the last four quarters. Find the quarter which produces low variations. Find the Department where variations are less.

9. The data displayed below represent the cost of electricity during July 2004 for a random sample of 50 one-bedroom apartments in a large city. (Raw data on utility Charges (Rs.)

Construct the frequency distribution and percentage distribution

Based on results around what amount does the monthly electricity cost seems to be concentrated?

10. The share prices of a company in Mumbai and Kolkata markets during the last 10 months are recorded below

Determine the arithmetic mean and standard deviation of prices of shares. In which market are the share prices more stable?

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