Advertisements
Advertisements
प्रश्न
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 exactly 4 defectives
Advertisements
उत्तर
Probability of getting a defective item
p = `5/100 = 1/20`
q = 1 – p
⇒ q = `1 - 1/20`
= `(20 - 1)/20`
q = `19/20` and n = 10
In binomial distribution
P(X = x) = nCxpxqn-x
Here (X = x)= `10"C"_x (1/20)^x (19/20)(10 - x)`
p(extactly 4 defectives) = p(X = 4)
= `10"c"_4 (1/20)^4 (9/20)^(10- 4)`
= `(10 xx 9 xx 8 xx 7)/(1 xx 2 xx 3 xx 4) xx (1/20)^4 (129/20)^6`
= `210 xx (19)^6/(20)^10`
= `(210 xx 4.648 xx 10^7)/(1.023 xx 10^3)`
= `(210 xx 4.648)/(1.023 xx 10^6)`
= `(210 xx 4.648)/1023000`
= `976.08/1023000`
= 0.000954
Let x = (19)6
log x = 6 log 19
= 6 × 1.2788
log x = 7.66728
Anti log (7.66728)
x = 4.648 × 107
APPEARS IN
संबंधित प्रश्न
Define Binomial distribution
In a particular university 40% of the students are having newspaper reading habit. Nine university students are selected to find their views on reading habit. Find the probability that all those selected have newspaper reading habit
If 18% of the bolts produced by a machine are defective, determine the probability that out of the 4 bolts chosen at random exactly one will be defective
Forty percent of business travellers carry a laptop. In a sample of 15 business travelers, what is the probability that 12 of the travelers will not have a laptop?
Forty percent of business travellers carry a laptop. In a sample of 15 business travelers, what is the probability that atleast three of the travelers have a laptop?
Derive the mean and variance of poisson distribution
Define Standard normal variate
Choose the correct alternative:
An experiment succeeds twice as often as it fails. The chance that in the next six trials, there shall be at least four successes is
Vehicles pass through a junction on a busy road at an average rate of 300 per hour. Find the probability that none passes in a given minute
The time taken to assemble a car in a certain plant is a random variable having a normal distribution of 20 hours and a standard deviation of 2 hours. What is the probability that a car can be assembled at this plant in a period of time. Less than 19.5 hours?
