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?
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
Define Bernoulli trials
If the probability of success is 0.09, how many trials are needed to have a probability of atleast one success as 1/3 or more?
Out of 750 families with 4 children each, how many families would be expected to have atmost 2 girls
Out of 750 families with 4 children each, how many families would be expected to have children of both sexes? Assume equal probabilities for boys and girls.
Forty percent of business travellers carry a laptop. In a sample of 15 business travelers, what is the probability that 12 of the travelers will not have a laptop?
An experiment succeeds twice as often as it fails, what is the probability that in next five trials there will be three successes
Define Standard normal variate
Write down the conditions in which the Normal distribution is a limiting case of binomial distribution
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:
The average percentage of failure in a certain examination is 40. The probability that out of a group of 6 candidates atleast 4 passed in the examination are
