Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
Given n = 5
p = `40/10 = 2/5`
q = 1 – p = `1 - 2/5 = (5-2)/5 = 3/5`
The binomial distribution P(X = x) = `15"c"_x (2/5)^x (3/5)^(15 - x)`
P(12 of the travels will not have a laptop)
= 1 – P(X = 12)
= `1 - 15"c"_12 (2/5)^12(3/5)^(15 - 12)`
= `1 - 15"c"_3 (2/5)^12 (3/5)^3`
= `1 - ((15 xx 14 xx 13)/(1 xx 2 xx 3)) [((2)^12 (3)^3)/(5)^15]`
= `1 - 455 ((4096 xx 27)/(3.055 xx 10^10))`
= `1 - 50319360/300550000000`
= `1 - 0.001647`
= 0.99835
APPEARS IN
संबंधित प्रश्न
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?
Forty percent of business travellers carry a laptop. In a sample of 15 business travelers, what is the probability that 3 will have a laptop?
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?
Consider five mice from the same litter, all suffering from Vitamin A deficiency. They are fed a certain dose of carrots. The positive reaction means recovery from the disease. Assume that the probability of recovery is 0.73. What is the probability that atleast 3 of the 5 mice recover
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:
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:
Choose the correct alternative:
If P(Z > z) = 0.8508 what is the value of z (z has a standard normal distribution)?
Choose the correct alternative:
If P(Z > z) = 0.5832 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. Between 20 and 22 hours?
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
