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 at least 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(at least 2 rejects) = P(X ≥ 2)
= `1 - "P"("X" < 2)`
= `1 - ["P"("X" = 0) + "P"("X" = 1)]`
= `1 - [(22)^10/(25)^10 + (30 xx (22)^9)/(25)^10]`
= `1 - {(22)^9/(25)^10 [22 + 30]}`
= `1 - {(52 xx (22)^9)/(25)^10}`
= `1 - {(52 xx 1.207 xx 10^12)/(9.528 xx 10^13)}`
= `1 - [(52 xx 1.207)/(9.528 xx 10)]`
= ` -[62.764/95.28]`
= `1 - 0.6587`
= 0.3413
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
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
Determine the binomial distribution for which the mean is 4 and variance 3. Also find P(X=15)
Assume that a drug causes a serious side effect at a rate of three patients per one hundred. What is the probability that atleast one person will have side effects in a random sample of ten patients taking the drug?
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]
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:
The parameters of the normal distribution f(x) = `(1/sqrt(72pi))"e"^(-(x - 10)^2)/72 - oo < x < oo`
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?
X is a normally distributed variable with mean µ = 30 and standard deviation σ = 4. Find P(X < 40)
