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 less than 1,950 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(less than 1950 hours)
P(X < 1950)
When x = 1950
z = `(1950 - 3040)/60`
= `(-90)/60`
= – 1.5
P(X < 1950) = P(Z < – 1.5) = P(Z > 1.5)
= 0.5 – 0.4332
= 0.068
Numbers of bulbs whose burning time is less than
1950
= 0.0668 × 2000
= 133.6
= 134 ......(approximately)
APPEARS IN
RELATED QUESTIONS
Define Binomial distribution
Mention the properties of binomial distribution.
If 18% of the bolts produced by a machine are defective, determine the probability that out of the 4 bolts chosen at random exactly one will be defective
If the heights of 500 students are normally distributed with mean 68.0 inches and standard deviation 3.0 inches, how many students have height greater than 72 inches
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:
A statistical analysis of long-distance telephone calls indicates that the length of these calls is normally distributed with a mean of 240 seconds and a standard deviation of 40 seconds. What proportion of calls lasts less than 180 seconds?
Choose the correct alternative:
Let z be a standard normal variable. If the area to the right of z is 0.8413, then the value of z must be:
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?
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
Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100. Raghul wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test. Raghul takes the test and scores 585. Will he be admitted to this university?
