Elementary Statistics and Computer Application

Application

Application

1. It is used in quality control statistics to count the number of defects of an item.
2. In biology, to count the number of bacteria.
3. In determining the number of deaths in a district in a given period, by rare disease.
4. The number of error per page in typed material.
5. The number of plants infected with a particular disease in a plot of field.
6. Number of weeds in particular species in different plots of a field

Example 4:

• Suppose on an average 1 house in 1000 in a certain district has a fire during a year. If there are 2000 houses in that district, what is the probability that exactly 5 houses will have a fire during the year? [given that e-2 = 0.13534]
Solution







The Poisson distribution is







= 0.036


Example 5


• If 2% of electric bulbs manufactured by a certain company are defective. Find the probability that in a sample of 200 bulbs i) less than 2 bulbs ii) more than 3 bulbs are defective.[e-4 = 0.0183]
 

Solution

• The probability of a defective bulb
• Given that n = 200 since p is small and n is large
• We use the Poisson distribution
• mean, m = np = 200 x 0.02 = 4
 
Now, Poisson Probability function,
i) Probability of less than 2 bulbs are defective

= P(X<2)
= P(x = 0) + P(x = 1)
= e- 4 + e- 4 (4)
= e- 4 (1 + 4) = 0.0183 x 5
= 0.0915

ii) Probability of getting more than 3 defective bulbs

P(x > 3) = 1-P(x £ 3)
= 1-{P(x = 0) + P(x =1) + P(x=2) + P(x=3)}

= 1-{0.0183 X (1 + 4 + 8 + 10.67)}
= 0.567