Question

Question:4

1. A new promotion by K2 has been developed with a goal of obtaining 90% new simcard connections among business firms. To evaluate the simcard sales, 20 are to be sold to business people in Kikuubo. If the 90% sales rate is correct, what is the probability that 18 or more of the sim cards will be sold to Kikuubo business men and women.

2. The life time of milk produced by Fresh Diary is normally distributed. The probability that a pack drawn from a Carton is defective is 0.1 and the success is 0.9, if a sample of 6 packs is taken, Find the probability that it will contain;

1. No defective packs   
2. 5 or 6 defective packs
3. Less than 3 defective packs

3. Using a relevant example, explain the Bernoulli trial              

Answer 1

a.

We use Binomial distribution in this case.

Probability mass function for Binomial distribution is :

'

where,

p = Probability of success

n = Sample size = Number of trials

x = Number of successes

In this case, we have :

n = 20

p = 90% = 0.90

Let X denote the number of sim cards will be sold to Kikuubo business men and women

Required probability = P(X>=18) = P(X=18)+P(X=19)+P(X=20)

So,

Note :

And 0! = 1

Solving above we get :

So,

Required probability = P(X=18) + P(X=19) + P(X=20) = 0.285+0.270+0.122 = 0.677

b.

Here we again use Binomial ditribution.

Let X denote the number of defective packs

We have,

p = Probability of defective pack = 0.1

n = Number of packs in sample = 6

i.

Probability that it will contain no defective packs = P(X=0)

ii.

Probability that it wil contain 5 or 6 defective packs = P(X=5) + P(X=6)

Hence,

Probability that it wil contain 5 or 6 defective packs = P(X=5) + P(X=6) = 0.0001+0.000001 = 0.000101

iii.

Probability that it will contain less than 3 defective packs = P(X<3) = P(X=0)+P(X=1)+P(X=2)

Probability that it will contain less than 3 defective packs = P(X<3) = P(X=0)+P(X=1)+P(X=2) = 0.531 + 0.354+0.098 = 0.984

c.

A random experiment whose outcomes are only of two types, say success S and failure F, is a Bernoulli trial.

Example :

Suppose there is an exam. The outcome of the exam would either be Passed or Failed.

So, lets take Passed as Success and Failed as Failure.

We take a random student and see what is the outcome of his exam. It would be either Passed or Failed.

In this we way we conduct a Bernoulli trial.