SaiBook.us Statistics

Lesson Example Discussion Quiz: Class Homework

Example

Title: Poisson distribution

Grade: 9-a Lesson: S4-L5

Explanation: The best way to understand statistics is by looking at some examples. Take turns and read each example for easy understanding.

Examples:

If 2% of electric bulbs manufactured by a certain company are defective find the probability that in a sample of 200 bulbs less than 2 bulbs are defective.

Step 1a

Arrange the given data

Explanation:

X denotes number of defective bulbs

Number of bulbs n = 200

Probability ( x defective bulb) p = 2%

p = 0.02

e = 2.718

x denotes 2 bulbs are defective

Step 1b

Calculating Probability

Explanation:

λ = np = 200(0.02)

λ = 4

\$P(X=x) = (e^(-λ) λ^x)/(x!)\$ i.e,x=0,1,2,… ∞

P(less than 2 bulbs are defective) = P(X<2)

P(X<2) = P(x=0) + P(x=1)

P(X<2) = \$((2.718)^(-4) 4^0)/(0!) + ((2.718)^(-4) 4^1)/(1!)\$

P(X<2) = \$(0.0183)(1)/1 + (0.0183)(4)/1\$

P(X<2) = 0.0915