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
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
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 the probability of success is 0.09, how many trials are needed to have a probability of atleast one success as 1/3 or more?
Out of 750 families with 4 children each, how many families would be expected to have atmost 2 girls
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]
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 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
Choose the correct alternative:
The average percentage of failure in a certain examination is 40. The probability that out of a group of 6 candidates atleast 4 passed in the examination are
Choose the correct alternative:
Forty percent of the passengers who fly on a certain route do not check in any luggage. The planes on this route seat 15 passengers. For a full flight, what is the mean of the number of passengers who do not check in any luggage?
Choose the correct alternative:
If P(Z > z) = 0.5832 what is the value of z (z has a standard normal distribution)?
