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ASSIGNMENTS V [THE BINOMIAL DISTRIBUTION]

Answer All Questions

1. In a certain gambling game, a player tosses a fair coin; if it falls head, he wins ¢1000. A player with ¢5000 tosses the coin six times. What is the probability that he will be left with ¢6000?

2. A large stock of resistors is known to have 20 per cent defectives. If 5 resistors are drawn

at random, determine:

a. The probabilities that (i) none is defective (ii) At least two are defective

b. The mean and standard deviation of the distribution of defects.

3. A firm, on average, receives 4 enquires per week relating to its new product.

Determine the probability that, the number of enquiries in any one week will be:

a. None b. two c. 3 or more

4. A machine delivered rods having a mean length of 18.0cm and standard deviation of 1.33mm. If the are normally distribution, determine the number of rods between 16.0mm 19.0mm long likly to occur in a run of 300.

5. A box contains a large number of transistors, 30 per cent of which are type A and the rest

type B. A random sample of 4 transistors is taken. Determine the probabilities that i. all

of type A ii. all of type B iii. Two of type A and two of type B

iv. three of type A and one of type B.

6. A milling machine produces products with an average of 4 per cent rejects. If a

random sample of 5 components is taken, determine the probability that it contains:

i. No reject ii. Fewer than 2 rejects

7. If 12 per cent of resistors produced in a run are defective, determine the probability

distribution of defectives in a random sample of 5 resistors.

8. Production of steel rollers includes, on average 8 per cent defectives. Determine the

probability that a random sample of 6 rollers contains:

a) No defectives b) fewer than 3 defectives

9. A machine produces an average 95 per cent of mouldings within tolerance values determine

the probability that a random sample of 5 mouldings shall contain;

a) No defective b) more than one defective

10. A large stock of resistors has 80 per cent within tolerance values. If 7 resistors are drawn

at random, determine the probability that

a) at least 5 are acceptable b) all 7 are acceptable

11. Twenty per cent of the output from a production run are rejects. In a random sample of 5

items, determine the probability of there being:

a) 0, 1, 2,3,4,5 rejects b) more than 1 reject c) fewer than 4 rejects

12. A production line produces 6 per cent defectives. For a random sample of 10 components,

determine the probability of obtaining:

a) No defective b) 2 defectives c) more than 3 defectives

13. Small metal springs are packed in boxes of 100 and 0.5 per cent of the total output springs

are defective. Determine the probability that any one box chosen at random shall have:

a) No defectives b) two or more defectives.

14. In a long production run, 1 per cent of the components are normally found to be defective.

In a random sample of 10 components, determine the probability that there will be fewer

than 2 defectives in the sample

## Answers

**Answer:**

ASSIGNMENTS V [THE BINOMIAL DISTRIBUTION]

Answer All Questions

1. In a certain gambling game, a player tosses a fair coin; if it falls head, he wins ¢1000. A player with ¢5000 tosses the coin six times. What is the probability that he will be left with ¢6000?

2. A large stock of resistors is known to have 20 per cent defectives. If 5 resistors are drawn

at random, determine:

a. The probabilities that (i) none is defective (ii) At least two are defective

b. The mean and standard deviation of the distribution of defects.

3. A firm, on average, receives 4 enquires per week relating to its new product.

Determine the probability that, the number of enquiries in any one week will be:

a. None b. two c. 3 or more

4. A machine delivered rods having a mean length of 18.0cm and standard deviation of 1.33mm. If the are normally distribution, determine the number of rods between 16.0mm 19.0mm long likly to occur in a run of 300.

5. A box contains a large number of transistors, 30 per cent of which are type A and the rest

type B. A random sample of 4 transistors is taken. Determine the probabilities that i. all

of type A ii. all of type B iii. Two of type A and two of type B

iv. three of type A and one of type B.

6. A milling machine produces products with an average of 4 per cent rejects. If a

random sample of 5 components is taken, determine the probability that it contains:

i. No reject ii. Fewer than 2 rejects

7. If 12 per cent of resistors produced in a run are defective, determine the probability

distribution of defectives in a random sample of 5 resistors.

8. Production of steel rollers includes, on average 8 per cent defectives. Determine the

probability that a random sample of 6 rollers contains:

a) No defectives b) fewer than 3 defectives

9. A machine produces an average 95 per cent of mouldings within tolerance values determine

the probability that a random sample of 5 mouldings shall contain;

a) No defective b) more than one defective

10. A large stock of resistors has 80 per cent within tolerance values. If 7 resistors are drawn

at random, determine the probability that

a) at least 5 are acceptable b) all 7 are acceptable

11. Twenty per cent of the output from a production run are rejects. In a random sample of 5

items, determine the probability of there being:

a) 0, 1, 2,3,4,5 rejects b) more than 1 reject c) fewer than 4 rejects

12. A production line produces 6 per cent defectives. For a random sample of 10 components,

determine the probability of obtaining:

a) No defective b) 2 defectives c) more than 3 defectives

13. Small metal springs are packed in boxes of 100 and 0.5 per cent of the total output springs

are defective. Determine the probability that any one box chosen at random shall have:

a) No defectives b) two or more defectives.

14. In a long production run, 1 per cent of the components are normally found to be defective.

In a random sample of 10 components, determine the probability that there will be fewer

than 2 defectives in the sample

**Step-by-step explanation:**

X and Y are partners sharing profits in the ratio of 3:2. They agree to take into partnership for Z 1/3rd share. For this purpose, goodwill is to be valued at two years' purchase of the average profit of last 4 years which were as follows:

Year ended on 31st March,2016 rs 150000(profit)

Year ending on 31st March ,2017 rs 120000(profit)

Year ending on 31st March, 2018 rs 180000(profit)

Year ending on 31st March, 2019 rs 170000(loss)

On 1st April, 2018 a Motor bike costing rs 50000 was purchased and debited to travelling expenses account , on which depreciation is to be charged @ 20% p.a. Calculate the value of goodwill.

(Ans.Goodwill rs 160000 ; average profit rs 80000)

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