Answer

Verified

449.1k+ views

**Hint:**The Poisson distribution is the discrete probability distribution of the number of events occurring in a given time period, given the average number of times the event occurs over that time period.

**Complete step by step solution**:

According to the question:

Probability of getting a defective bottle (p) = $ 0.1\% = \dfrac{{0.1}}{{100}} = 0.001 $

And number of bottles in box (n) = 500

Therefore according to the poisson distribution

$ \lambda = np = 500 \times 0.001 = 0.5 $

And number of boxes (N) = 100

And from poisson distribution we know that

P(x) $ = \dfrac{{{e^{ - \lambda }}{\lambda ^x}}}{{x!}} $

Therefore number of boxes with no defective bottles (x=0) =

$

100 \times p(x = 0) \\

= 100 \times \dfrac{{{e^{ - \lambda }}{\lambda ^x}}}{{x!}}...........(x = 0) \\

= 100 \times \dfrac{{{e^{ - 0.5}}({{0.5}^0})}}{{0!}} \\

= 100 \times {e^{ - 0.5}} \\

$

Hence the required number of boxes with 0 defective bottles = $ 100 \times {e^{ - 0.5}} $

**Note:**In poisson distribution $ \lambda $= np here $ \lambda $ is the mean of the given distribution and n is the number of units.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths