Advertisements
Advertisements
Question
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?
Advertisements
Solution
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(probability that 3 will have a laptop) = P(X = 3)
= `15"c"_3 (2/5)^3 (/5)^(15 - 3)`
= `(15 xx 14 xx 13)/(1 xx 2 xx 3) xx (2)^3/(5)^3 xx (3)^12/(5)^12`
= `455 xx (8 xx 5.311 xx 10^5)/(5)^15`
= `(3640 xx 5.311 xx 10^5)/(3.055 xx 10^10)`
= `(3640 xx 5.311)/(3.055 xx 10^5)`
= `19332.04/305500`
= 0.06328
APPEARS IN
RELATED QUESTIONS
Derive the mean and variance of binomial distribution
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 exactly three defectives
Defects in yarn manufactured by a local mill can be approximated by a distribution with a mean of 1.2 defects for every 6 metres of length. If lengths of 6 metres are to be inspected, find the probability of less than 2 defects
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
It is given that 5% of the electric bulbs manufactured by a company are defective. Using poisson distribution find the probability that a sample of 120 bulbs will contain no defective bulb
In a photographic process, the developing time of prints may be looked upon as a random variable having the normal distribution with a mean of 16.28 seconds and a standard deviation of 0.12 second. Find the probability that it will take less than 16.35 seconds to develop prints
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) = 0.5832 what is the value of z (z has a standard normal distribution)?
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
People’s monthly electric bills in Chennai are normally distributed with a mean of ₹ 225 and a standard deviation of ₹ 55. Those people spend a lot of time online. In a group of 500 customers, how many would we expect to have a bill that is ₹ 100 or less?
