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
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