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 at least 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(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
RELATED QUESTIONS
Mention the properties of binomial distribution.
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
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
If 18% of the bolts produced by a machine are defective, determine the probability that out of the 4 bolts chosen at random exactly one will be defective
Write the conditions for which the poisson distribution is a limiting case of binomial distribution
The average number of customers, who appear in a counter of a certain bank per minute is two. Find the probability that during a given minute no customer appears
Choose the correct alternative:
In a parametric distribution the mean is equal to variance is
Choose the correct alternative:
Which of the following cannot generate a Poisson distribution?
Choose the correct alternative:
If the area to the left of a value of z (z has a standard normal distribution) is 0.0793, what is the value of z?
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?
