Advertisements
Advertisements
प्रश्न
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 atleast two-third have newspaper reading habit
Advertisements
उत्तर
Let p to the probability of having newspaper reading habit
p = `40/100 = 2/5`
q = 1 – p
= `1 2/5`
= `(5 - 2)/5`
= `3/5` and n = 9
In the binomial distribution p(x = 4) = ncx pxqn-r
The binomial distribution P(x) = `9"C"_x (2/5)^x (3/5)^(9 - x)`
P(at least two third have newspaper reading habit)
`"P"(x ≥ 9 xx 2/3)`
= `"P"(x ≥ 6)`
= P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)
= `9"c"_6 (2/5)^6 (3/5)^(9 - 6) + 9"c"_7 (2/7)^7 (3/5)^(9 - 7) + 9"c"_8 (2/5)^8 (3/5)^(9 - 8) + 9"c"_9 (2/5)^9 (3/5)^(9 - 9)`
= `9"c"_3 (2/5)^6 (3/5)^3 + 9"c"_2 (2/5)^7 (3/5)^2 + 9"c"_1 (2/5)^8 (3/5)^1 + 1(2/5)^9 (3/5)^0`
= `(9 xx 8 xx 7)/(1 xx 2 xx 3) xx [((2)^6 xx (3)^3)/(5)^9] + (9 xx 8)/(1 xx 2) [((2)^7 xx (3)^2)/(5)^9] + 9 xx [((2)^8 xx 3)/(5)^9] + (2)^9/(5)^9`
= `84 xx ((64 xx 27)/(5)^9) + 36 [(128 xx 9)/(5)^9] + 9 xx [(256 xx 3)/(5)^9] + [512/(5)^9]`
= `145152/(5)^9 + 41472/(5)^9 + 6912/(5)^9 + 512/(5)^9`
= `(145152 + 41472 + 6912 + 512)/(5)^9`
= `194048/195312`
= 0.09935
APPEARS IN
संबंधित प्रश्न
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 4 defectives
Write any 2 examples for Poisson distribution
The average number of phone calls per minute into the switchboard of a company between 10.00 am and 2.30 pm is 2.5. Find the probability that during one particular minute there will be atleast 5 calls
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 1,920 hours but less than 2,100 hours
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
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 between 65 and 71 inches
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:
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?
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?
