ASSIGNMENT
ASSIGNMENT (2015-16)
1. During a socio-economic survey conducted in a rural area, the concerned authorities came to the conclusion that mean level of income in the area was Rs 150 per month with a standard deviation of Rs 20 and that income is approximately normally distributed. The total population of the area was 4000. Compute the number of people who fell into the following categories:
(i) monthly income less than Rs 50
(ii) monthly income greater than Rs 100 but less than or equal to Rs 150.
(iii) monthly income greater than Rs 250.
2. The demand of a product is approximately normally distributed with an average demand of 300 units per month. The probability of demand being less than 280 units is 0.025. What is the probability that demand is more than 315 units?
3. Approximately 30% of the time demand of a product is more than 250 units, and 20% of the time demand is less than 200 units. What is the average demand? What is the standard deviation of demand? (Demand can be assumed to follow a normal distribution) The demand of a product is observed to vary from one quarter to the other. The demand of each quarter can be assumed to follow a normal distribution with means and standard deviations given below:
Demand
Quarter
Mean
Standard Deviation
1
300
10
2
250
10
3
400
13
4
450
15
What is the probability that the annual demand will be more than 1450 units? Demands in the four quarters are independent.
4. What should be the standard deviation of a bolt-making machine if 94% of the bolt lengths are to be in an interval extending from 0.0047 m.m. to the left of the mean to 0.0047 to the right of the mean.
5. The average time before the gear train of an automobile needs a major overhaul is 56 months with standard deviation of 16 months. The manufacturer wishes to warranty these gear trains. For how many months should the manufacturer warrant gear trains to limit the number of warranty overhauls to no
1. During a socio-economic survey conducted in a rural area, the concerned authorities came to the conclusion that mean level of income in the area was Rs 150 per month with a standard deviation of Rs 20 and that income is approximately normally distributed. The total population of the area was 4000. Compute the number of people who fell into the following categories:
(i) monthly income less than Rs 50
(ii) monthly income greater than Rs 100 but less than or equal to Rs 150.
(iii) monthly income greater than Rs 250.
2. The demand of a product is approximately normally distributed with an average demand of 300 units per month. The probability of demand being less than 280 units is 0.025. What is the probability that demand is more than 315 units?
3. Approximately 30% of the time demand of a product is more than 250 units, and 20% of the time demand is less than 200 units. What is the average demand? What is the standard deviation of demand? (Demand can be assumed to follow a normal distribution) The demand of a product is observed to vary from one quarter to the other. The demand of each quarter can be assumed to follow a normal distribution with means and standard deviations given below:
Demand
Quarter
Mean
Standard Deviation
1
300
10
2
250
10
3
400
13
4
450
15
What is the probability that the annual demand will be more than 1450 units? Demands in the four quarters are independent.
4. What should be the standard deviation of a bolt-making machine if 94% of the bolt lengths are to be in an interval extending from 0.0047 m.m. to the left of the mean to 0.0047 to the right of the mean.
5. The average time before the gear train of an automobile needs a major overhaul is 56 months with standard deviation of 16 months. The manufacturer wishes to warranty these gear trains. For how many months should the manufacturer warrant gear trains to limit the number of warranty overhauls to no