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
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
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
An experiment succeeds twice as often as it fails, what is the probability that in next five trials there will be at least three successes
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).
In a distribution 30% of the items are under 50 and 10% are over 86. Find the mean and standard deviation of the distribution
Choose the correct alternative:
Normal distribution was invented by
Choose the correct alternative:
If for a binomial distribution b(n, p) mean = 4 and variance = 4/3, the probability, P(X ≥ 5) is equal to
Choose the correct alternative:
The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of ₹ 180,000 and a standard deviation of ₹ 10,000. What is the probability that a randomly selected newly qualified CA will earn between ₹ 165,000 and ₹ 175,000?
Choose the correct alternative:
A statistical analysis of long-distance telephone calls indicates that the length of these calls is normally distributed with a mean of 240 seconds and a standard deviation of 40 seconds. What proportion of calls lasts less than 180 seconds?
Vehicles pass through a junction on a busy road at an average rate of 300 per hour. What is the expected number passing in two minutes?
The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000 and a standard deviation of $20,000. What percent of people earn less than $40,000?
