Advertisements
Advertisements
Question
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?
Advertisements
Solution
Let x denotes the time taken to assemable cars mean µ = 20 hours and S.D σ = 2 hours
The standard normal variate
z = `(x - mu)/sigma`
= `(x - 20)/2`
P(less than 19.5 hours) = P(X < 19.5)
When x = 19.5
z = `19.5/2`
= `(-0.5)/2`
= 0.25
P(X < 19.5) = P(Z < – 0.25)
= P(`-oo` < z < 0) – P(– 0.25 < z < 0)
= 0.5 – P(0 < z < 0.25)
= 0.5 – 0.0987
= 0.4013
APPEARS IN
RELATED QUESTIONS
In a particular university 40% of the students are having newspaper reading habit. Nine university students are selected to find their views on reading habit. Find the probability that none of those selected have newspaper reading habit
Out of 750 families with 4 children each, how many families would be expected to have atleast one boy
In a distribution 30% of the items are under 50 and 10% are over 86. Find the mean and standard deviation of the distribution
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:
A manufacturer produces switches and experiences that 2 percent switches are defective. The probability that in a box of 50 switches, there are atmost two defective is :
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:
Monthly expenditure on their credit cards, by credit cardholders from a certain bank, follows a normal distribution with a mean of ₹ 1,295.00 and a standard deviation of ₹ 750.00. What proportion of credit cardholders spend more than ₹ 1,500.00 on their credit cards per month?
The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000 and a standard deviation of $20,000. What percent of people earn more than $75,000
The birth weight of babies is Normally distributed with mean 3,500g and standard deviation 500g. What is the probability that a baby is born that weighs less than 3,100g?
