Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
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 three defectives
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
If 18% of the bolts produced by a machine are defective, determine the probability that out of the 4 bolts chosen at random none will be defective
Out of 750 families with 4 children each, how many families would be expected to have atmost 2 girls
An experiment succeeds twice as often as it fails, what is the probability that in next five trials there will be three successes
A car hiring firm has two cars. The demand for cars on each day is distributed as a Poison variate, with mean 1.5. Calculate the proportion of days on which neither car is used
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 at most 3 accidents
In a photographic process, the developing time of prints may be looked upon as a random variable having the normal distribution with a mean of 16.28 seconds and a standard deviation of 0.12 second. Find the probability that it will take less than 16.35 seconds to develop prints
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. Between 20 and 22 hours?
X is a normally distributed variable with mean µ = 30 and standard deviation σ = 4. Find P(X > 21)
