Advertisements
Advertisements
प्रश्न
A manufacturer of metal pistons finds that on the average, 12% of his pistons are rejected because they are either oversize or undersize. What is the probability that a batch of 10 pistons will contain no more than 2 rejects?
Advertisements
उत्तर
In a binomial distribution
n = 10
p = `12/100 = 3/25`
q = – p = `1 - 3/25` q = = `22/25`
PX = x) = ncxpxqn-x
P(no more than 2 rejects)
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
= `""^10"C"_0 (3/25)^0 (22/25)^(10 - 0) + ""^10"C"_1 (3/25)^1 (22/25)^(10 - 1) + ""^10"C"_2 (3/25)^2 + (22/25)^(10 - 2)`
= `(1)(1) (22/25)^10 + 10 ((3 xx (22)^9)/((25)^10)) + (10 xx 9)/(1 xx 2) (3/25)^2 (22/25)^8`
= `((22)^10 + (30 xx (22)^9) + 405(22)^8)/(25)^10`
= `((22)^8 [(22)^2 + (30 xx 22) + 405])/(25)^10`
= `(5.486 xx 10^10 xx 1549)/(9.5288 xx 10^13`
= `(5.486 xx 1549)/(9.528 xx 10^3)`
= `(5.486 xx 1549)/9528`
= 0.89187
APPEARS IN
संबंधित प्रश्न
Forty percent of business travellers carry a laptop. In a sample of 15 business travelers, what is the probability that 3 will have a laptop?
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 average number of phone calls per minute into the switchboard of a company between 10.00 am and 2.30 pm is 2.5. Find the probability that during one particular minute there will be no phone at all
The average number of phone calls per minute into the switchboard of a company between 10.00 am and 2.30 pm is 2.5. Find the probability that during one particular minute there will be atleast 5 calls
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
Time taken by a construction company to construct a flyover is a normal variate with mean 400 labour days and a standard deviation of 100 labour days. If the company promises to construct the flyover in 450 days or less and agree to pay a penalty of ₹ 10,000 for each labour day spent in excess of 450. What is the probability that the company pay a penalty of at least ₹ 2,00,000?
Choose the correct alternative:
In a large statistics class, the heights of the students are normally distributed with a mean of 172 cm and a variance of 25 cm. What proportion of students is between 165cm and 181 cm in height?
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 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 between $45,000 and $65,000?
The birth weight of babies is Normally distributed with mean 3,500g and standard deviation 500g. What is the probability that a baby is born that weighs less than 3,100g?
