Advertisements
Advertisements
Question
Defects in yarn manufactured by a local mill can be approximated by a distribution with a mean of 1.2 defects for every 6 metres of length. If lengths of 6 metres are to be inspected, find the probability of less than 2 defects
Advertisements
Solution
Given n = 6
Mean np = 1.2
⇒ 6p = 1.2
p = `1.2/6 "p" = 0.2`or p = `1/5`
q = 1 – p = `1 - 1/5`
∴ q = `4/5`
The binomial distribution
p(x) = 6Cx (0.2)x(0.8)6-x
p(x < 2) = p(x = 0) + p(x = 1)
= `6"c"_0 (1/5)^0 (4/5)^(6 - 0) + 6"c"_1 (1/5)^1 (4/5)^(6 - 1)`
= `(1)(1)(4/5)^6 + 6(1/5)(4/5)5`
= `(4)^6/(5)^6 + (6 xx (4)^5)/(5)^6`
= `4096/15625 + ((6 xx 1024)/(15625))`
= `(4096 + 6144)/15625`
= `10240/15625`
= 0.65536
APPEARS IN
RELATED QUESTIONS
Define Binomial distribution
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of 2 successes
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 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 exactly 3 calls
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
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 three or more customers appear
In a test on 2,000 electric bulbs, it was found that bulbs of a particular make, was normally distributed with an average life of 2,040 hours and standard deviation of 60 hours. Estimate the number of bulbs likely to burn for less than 1,950 hours
Choose the correct alternative:
In turning out certain toys in a manufacturing company, the average number of defectives is 1%. The probability that the sample of 100 toys there will be 3 defectives is
Choose the correct alternative:
If P(Z > z) = 0.5832 what is the value of z (z has a standard normal distribution)?
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?
