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
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 none of those selected have newspaper reading habit
Out of 750 families with 4 children each, how many families would be expected to have children of both sexes? Assume equal probabilities for boys and girls.
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of 2 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
Choose the correct alternative:
The parameters of the normal distribution f(x) = `(1/sqrt(72pi))"e"^(-(x - 10)^2)/72 - oo < x < oo`
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:
Cape town is estimated to have 21% of homes whose owners subscribe to the satellite service, DSTV. If a random sample of your home is taken, what is the probability that all four homes subscribe to DSTV?
If electricity power failures occur according to a Poisson distribution with an average of 3 failures every twenty weeks, calculate the probability that there will not be more than one failure during a particular week
