Advertisements
Advertisements
प्रश्न
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
उत्तर
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
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
The mean of a binomial distribution is 5 and standard deviation is 2. Determine the distribution
A car hiring firm has two cars. The demand for cars on each day is distributed as a Posison variate, with mean 1.5. Calculate the proportion of days on which some demand is refused
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).
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 less than or equal to 64 inches
Choose the correct alternative:
If Z is a standard normal variate, the proportion of items lying between Z = – 0.5 and Z = – 3.0 is
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:
In a large statistics class, the heights of the students are normally distributed with a mean of 172 cm and a variance of 25 cm. What proportion of students is between 165cm and 181 cm in height?
Choose the correct alternative:
If P(Z > z) = 0.8508 what is the value of z (z has a standard normal distribution)?
The time taken to assemble a car in a certain plant is a random variable having a normal distribution of 20 hours and a standard deviation of 2 hours. What is the probability that a car can be assembled at this plant in a period of time. Less than 19.5 hours?
