BINOMIAL DISTRIBUTION EXAMPLES - Weebly



BINOMIAL DISTRIBUTION EXAMPLES

1. A coin is tossed six times . What is the prob. of 4 or more heads.?

2. Assuming that half the population is veg and assuming that 100 investigators can take 10 samples find ( a ) the probability that 3 or less persons are veg. ( b ) how many investigators would report 3 or less persons are veg

3. If the prob. of defective bolts is 0.1 , find the mean and s.d of a sample of 500 for defective bolts

4. The incidence of a certain disease is such that 20% of workers suffer from it. If 10 workers are selected what is the prob. of ( a ) exactly 2 workers have the disease

( b ) not more than 2 workers have the disease

5. A manufacturer producing medicine bottles finds that 0.1% of the bottles are defectives. The bottles are packed in boxes of 500 bottles. A drug dealer buys 100 boxes . Using Poisson distn. Find how many boxes will have

( a ) no defectives

( b ) at lest 2 defectives .

6. Out of 320 families with 5 children each what percentage be expected to have ( a ) 2 boys and 3 girls ( b ) at least one boy

B (n, p ) = nCr pr q(n-r) mean= np s.d = (npq)1/2

POISSON DISTRIBUTION EXAMPLES

1. In a certain factory manufacturing blades there is 0.2 chance of defective prodn. . The blades are put in packets of 10. Using Poisson distn. calculate approx no of packets containing exactly 2 defective blades in a consignment of 10,000 packets.

2. Suppose that a manufactured product has 2 defects per unit of product inspected. Using Poisson distn. Calculate the probs. of 0 defect , 3 defects and 4 defects.

The Poisson Distn P ( r ) = e-m m r/r! r= 0,1,2 …., m= mean or np

np=m The average occurrences can be as follows

N Po = N e-m

N P1 = N Po x m/1

N P2 = N P1x m/2

NORMAL DISTRIBUTION

1. Of a large group of men , 5% are under 60 inches , and 40% are between 60 and 65 inches. Assuming normal distn find mean and s.d.

2. A project yields an average cash flow of Rs. 500 lakhs with s.d. Rs 60 lakhs. Calculate the following probs.

( a ) Cash flow will be more than Rs. 560 lakhs

( b ) Cash flow will be less than Rs. 420 lakhs

( c ) Cash flow will be between Rs 460 and Rs. 560 lakhs

( d ) Cash flow will be more than Rs. 660 lakhs

3. The customer accounts of a store have average balance of Rs.480 and s.d. 160. assuming normal distn Calculate

( i ) What proportion of accounts is over Rs 600

( ii ) What proportion of accounts is between Rs 400 and Rs 600

( iii ) What proportion of accounts is between Rs 240 and Rs 360

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download