Advertisements
Advertisements
Question
If the probability that a fluorescent light has a useful life of at least 600 hours is 0.9, find the probabilities that among 12 such lights at least 11 will have a useful life of at least 600 hours
Solution
Let p be the probability of the useful life hours of a fluorescent light.
n = 12
p = 0.9
X = B(n, p)
q – 1 – p = 0.1
P(X = x) = ⁿCx px qn-x, x = 0, 1, 2, …. n
At least 11
P(X ≥ 11) = P(X = 11) + P(X = 12)
= 12C11 (0.9)11 (0.1)1 + 12C12 (0.9)12 (0.1)°
= 12 × (0.9)11 × 0.1 + 1 × (0.9)12 × 1
= (0.9)11 (12 × 0.1 × 0.9)
= (0.9)11 (1.2 + 0.9)
= (2.1) (0.9)11
APPEARS IN
RELATED QUESTIONS
Compute P(X = k) for the binomial distribution, B(n, p) where
n = 10, p = `1/5`, k = 4
The probability that Mr.Q hits a target at any trial is `1/4`. Suppose he tries at the target 10 times. Find the probability that he hits the target exactly 4 times
The probability that Mr.Q hits a target at any trial is `1/4`. Suppose he tries at the target 10 times. Find the probability that he hits the target at least one time
Using binomial distribution find the mean and variance of X for the following experiments.
A fair coin is tossed 100 times, and X denote the number of heads
Using binomial distribution find the mean and variance of X for the following experiments.
A fair die is tossed 240 times and X denotes the number of times that four appeared
The probability that a certain kind of component will survive a electrical test is `3/4`. Find the probability that exactly 3 of the 5 components tested survive
A retailer purchases a certain kind of electronic device from a manufacturer. The manufacturer indicates that the defective rate of the device is 5%. The inspector of the retailer randomly picks 10 items from a shipment. What is the probability that there will be at least one defective item
A retailer purchases a certain kind of electronic device from a manufacturer. The manufacturer indicates that the defective rate of the device is 5%. The inspector of the retailer randomly picks 10 items from a shipment. What is the probability that there will be exactly two defective items?
If the probability that a fluorescent light has a useful life of at least 600 hours is 0.9, find the probabilities that among 12 such lights exactly 10 will have a useful life of at least 600 hours
If the probability that a fluorescent light has a useful life of at least 600 hours is 0.9, find the probabilities that among 12 such lights at least 2 will not have a useful life of at least 600 hours
The mean and standard deviation of a binomial variate X are respectively 6 and 2. Find the probability mass function
The mean and standard deviation of a binomial variate X are respectively 6 and 2. Find P(X = 3)
The mean and standard deviation of a binomial variate X are respectively 6 and 2. Find P(X ≥ 2)
If X ~ B(n, p) such that 4P(X = 4) = P(x = 2) and n = 6. Find the distribution, mean and standard deviation of X
In a binomial distribution consisting of 5 independent trials, the probability of 1 and 2 successes are 0.4096 and 0.2048 respectively. Find the mean and variance of the random variable
Choose the correct alternative:
If in 6 trials, X is a binomial variable which follows the relation 9P(X = 4) = P(X = 2), then the probability of success is
