Advertisements
Advertisements
Question
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 more than 2,150 hours
Advertisements
Solution
Let x denote the burning of the bulb follows normal distribution with mean 2,040 and standard deviation 60 hours.
Here m = 2040
σ = 60
N = 2000
The standard normal variate
z = `(x - mu)/sigma`
= `(x - 2040)/60`
P(morethan 2,150 hours)
P(X > 2150)
When x = 2150
z = `(2150 - 2040)/60`
= `110/60`
= 1.833
P(X > 2150) = P(Z > 1.833)
= P(0 < z < `oo`) – P(0 < z < 1.833)
= 0.5 – 0.4664
= 0.0336
∴ Number of bulbs whose burning time is more than 2150 hours
= 0.0336 × 2000
= 67.2
= 67 .......(approximately)
APPEARS IN
RELATED QUESTIONS
Determine the binomial distribution for which the mean is 4 and variance 3. Also find P(X=15)
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?
Define Poisson distribution
Assuming that a fatal accident in a factory during the year is 1/1200, calculate the probability that in a factory employing 300 workers there will be at least two fatal accidents in a year, (given e-0.25 = 0.7788).
In a distribution 30% of the items are under 50 and 10% are over 86. Find the mean and standard deviation of the distribution
Time taken by a construction company to construct a flyover is a normal variate with mean 400 labour days and a standard deviation of 100 labour days. If the company promises to construct the flyover in 450 days or less and agree to pay a penalty of ₹ 10,000 for each labour day spent in excess of 450. What is the probability that the company takes at most 500 days to complete the flyover?
Choose the correct alternative:
Normal distribution was invented by
Choose the correct alternative:
If X ~ N(9, 81) the standard normal variate Z will be
Choose the correct alternative:
An experiment succeeds twice as often as it fails. The chance that in the next six trials, there shall be at least four successes is
Choose the correct alternative:
The starting annual salaries of newly qualified chartered accountants (CA’s) in South Africa follow a normal distribution with a mean of ₹ 180,000 and a standard deviation of ₹ 10,000. What is the probability that a randomly selected newly qualified CA will earn between ₹ 165,000 and ₹ 175,000?
