Advertisements
Advertisements
Question
If the probability of success is 0.09, how many trials are needed to have a probability of atleast one success as 1/3 or more?
Advertisements
Solution
Given p = 0.09 ......(success)
q = 0.91 .......(failure)
We have to find number of trials ‘n.’
According to the problem,
P(X ≥ 1 ) > `1/3`
We must have atleast one success
1 – P(X < 1) > `1/3`
1 – P(X = 0) > `1/3`
or
P(X = 0) < `2/3`
Using p.m.f, we have,
`""^"n""C"_0 (0.09)^0 (0.91)^"n" < 2/3`
`(0.91)"n" < 2/3`
We can use log tables to calculate or by trial method try for n = 1, 2,…… using calculator.
We observe that `(0.91)5 < 2/3`.
Thus we need minimum 5 trial or more.
APPEARS IN
RELATED QUESTIONS
Define Binomial distribution
If 5% of the items produced turn out to be defective, then find out the probability that out of 20 items selected at random there are find the mean and variance
It is given that 5% of the electric bulbs manufactured by a company are defective. Using poisson distribution find the probability that a sample of 120 bulbs will contain no defective bulb
The distribution of the number of road accidents per day in a city is poisson with mean 4. Find the number of days out of 100 days when there will be no accident
The distribution of the number of road accidents per day in a city is poisson with mean 4. Find the number of days out of 100 days when there will be atleast 2 accidents
The average number of customers, who appear in a counter of a certain bank per minute is two. Find the probability that during a given minute three or more customers appear
Choose the correct alternative:
If Z is a standard normal variate, the proportion of items lying between Z = – 0.5 and Z = – 3.0 is
Choose the correct alternative:
In turning out certain toys in a manufacturing company, the average number of defectives is 1%. The probability that the sample of 100 toys there will be 3 defectives is
Choose the correct alternative:
The parameters of the normal distribution f(x) = `(1/sqrt(72pi))"e"^(-(x - 10)^2)/72 - oo < x < oo`
Choose the correct alternative:
The average percentage of failure in a certain examination is 40. The probability that out of a group of 6 candidates atleast 4 passed in the examination are
