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 atleast two 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(atleast two defectives)
= p(x ≥ 2)
= p(x = 2) = p(x = 3) + ………….. + p(x = 10)
= 1 – p(x < 2)
= 1 – {p(x = 0) + p(x = 1)}
= `1 - [10"c"_0 (1/20)^0 (19/20)^(10 -0) + 10"C"_1 (1/20)(19/20)^(10 - 1)]`
= `1 - {(19)^10/(20)^10 + (10 xx 1/20) + (19)^9/(20)^9}`
= `1 - {(19)^9/(20)^10 + (10(19)^9)/(20)^10}`
= `1 - {(19)^9/(20)^9 [19 + 10]}`
= `1 - [(3.229 xx 10^11 (29))/(1.023 xx 10^13)]`
= `1 - [(3.229 xx (29))/(1.023 xx 10^2)]`
= `1 - [93.641/102.3]`
= `1- 0.9154`
= 0.0846
Let x = (19)9
log x = 9 log 19
= 9 × 1.2788
= 11.5092
x = Anti log 11.5092
= 3.229 × 1011
APPEARS IN
संबंधित प्रश्न
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 atleast two-third have newspaper reading habit
Out of 750 families with 4 children each, how many families would be expected to have children of both sexes? Assume equal probabilities for boys and girls.
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?
Define Poisson distribution
The mortality rate for a certain disease is 7 in 1000. What is the probability for just 2 deaths on account of this disease in a group of 400? [Given e–2.8 = 0.06]
Assuming that a fatal accident in a factory during the year is 1/1200, calculate the probability that in a factory employing 300 workers there will be at least two fatal accidents in a year, (given e-0.25 = 0.7788).
If the heights of 500 students are normally distributed with mean 68.0 inches and standard deviation 3.0 inches, how many students have height between 65 and 71 inches
Choose the correct alternative:
Forty percent of the passengers who fly on a certain route do not check in any luggage. The planes on this route seat 15 passengers. For a full flight, what is the mean of the number of passengers who do not check in any luggage?
Hospital records show that of patients suffering from a certain disease 75% die of it. What is the probability that of 6 randomly selected patients, 4 will recover?
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?
