# ASSIGNMENT

**Topics:**Normal distribution, Standard deviation, Poisson distribution

**Pages:**5 (1045 words)

**Published:**August 9, 2015

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 more than 2.28% of the automobiles sold? Assume normal distribution for number of months before an overhaul is required.

6. The average marks secured by PGP-I students in Section ‘A’ in QAM-I course was 80 and the coefficient of variation was 5%. If the top 2% of the students registered for the course are to receive A+ grade, then what is the minimum mark a student must get in order to receive A+ grade?

P. T. O.

8.Suppose taxicab arrivals from 3 to 5 p.m. follow a Poisson process. If the cabs arrive at an average rate of 18 per hour, (a) what is the probability that a person will have to wait up to 5 minutes for cab? (b) What is the probability that a person will have to wait between 5 and 10 minutes for cab?

9.An investment manager for UTI receives an average of 12 telephone calls per 8-hour day from major investors. Assuming calls are a Poisson process, what is the probability that the manager will not be interrupted by a call during a meeting lasting one hour?

10.The average number of customers arriving in a supermarket is 30 per hour. What is the probability that the length of time between a pair of successive arrivals of customers exceeds 3 minutes?

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ASSIGNMENT

1.The cylinder-making machine has standard deviation of 0.5 m.m. Assuming diameters are normally distributed, determine the process mean such that only 2.5% of the cylinders have diameters of 25.48 m.m. or more? [Ans: 24.5 m.m.] 2..The length of time between breakdowns of an essential piece of equipment is an important factor in deciding on the amount of auxiliary equipment needed to assure continuous service. A machine room foreman believes the time between breakdowns of a particular eldectrical generator is approximated by an exponential distribution with mean equal to 10 days. (i) If the generator broke down today, what is the probability...

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