RD Sharma - Mathematics (Volume 2)

Book: RD Sharma - Mathematics (Volume 2)

Chapter: 33. Binomial Distribution

Subject: Maths - Class 12th

Q. No. 4 of Exercise 33.2

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

4

Find the binomial distribution when the sum of its mean and variance for 5 trials is 4.8.

Given that,


n = 5


Also, Mean+ Variance = 4.8


⇒np + npq = 4.8


⇒np(1+q) = 4.8


⇒5p(1+q) = 4.8


⇒5(1 - q)(1+q) = 4.8 [Since, p + q = 1]


⇒5(1 - q2) = 4.8









The required binomial distribution is given by,



Chapter Exercises

Exercise 33.2
Exercise 33.1
Very Short Answer
MCQ

More Exercise Questions

1

Can the mean of a binomial distribution be less than its variance?
2

Determine the binomial distribution whose mean is 9 and variance 9/4.
3

If the mean and variance of a binomial distribution are respectively 9 and 6, find the distribution.
4

Find the binomial distribution when the sum of its mean and variance for 5 trials is 4.8.
5

Determine the binomial distribution whose mean is 20 and variance 16.
6

In a binomial distribution, the sum and product of the mean and the variance are 25/3 and 50/3 respectively. Find the distribution.
7

The mean of a binomial distribution is 20, and the standard deviation 4. Calculate the parameters of the binomial distribution.
8

If the probability of a defective bolt is 0.1, find the (i) mean and (ii) standard deviation for the distribution of bolts in a total of 400 bolts.
9

Find the binomial distribution whose mean is 5 and variance 10/3.
10

If on an average 9 ships out of 10 arrive safely to ports, find the mean and S.D. of ships returning safely out of a total of 500 ships.
11

The mean and variance of binomial variate with parameters n and p are 16 and 8 respectively. Find P (X = 0), P (X = 1) and P (X ≥ 2).
12

In eight throws of a die 5 or 6 is considered a success, find the mean number of successes and the standard deviation.
13

Find the expected number of boys in a family with 8 children, assuming the sex distribution to be equally probable.
14

The probability is 0.02 that an item produced by a factory is defective. A shipment of 10,000 items is sent to its warehouse. Find the expected number of defective items and the standard deviation.
15

A die is thrown thrice. A success is 1 or 6 in a throw. Find the mean and variance of the number of successes.
16

If a random variable X follows a binomial distribution with mean 3 and variance 3/2, find P(X ≤ 5).
17

If X follows a binomial distribution with mean 4 and variance 2, find P(X ≥ 5).
18

The mean and variance of a binomial distribution are 4/3 and 8/9 respectively. Find P (X ≥ 1).
19

If the sum of the mean and variance of a binomial distribution for 6 trials is 10/3, find the distribution.
20

A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability distribution of a number of successes and hence find its mean.
21

Find the probability distribution of the number of doublets in three throws of a pair of dice and hence find its mean.
22

From a lot of 15 bulbs which include 5 defectives, a sample of 4 bulbs is drawn one by one with replacement. Find the probability distribution of a number of defective bulbs. Hence, find the mean of the distribution.
23

A die is thrown three times. Let X be the number of two’s seen. Find the expectation of X.
24

A die is tossed twice. A ‘success’ is getting an even number on a toss. Find the variance of some successes.
25

Three cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of spades. Hence, find the mean of the distribution.
26

An urn contains 3 white and 6 red balls. Four balls are drawn one by one with replacement from the urn. Find the probability distribution of the number of red balls drawn. Also, find the mean and variance of the distribution.
27

Five bad oranges are accidentally mixed with 20 good ones. If four oranges are drawn one by one successively with replacement, then find the probability distribution of number of bad oranges drawn. Hence, find the mean and variance of the distribution.
28

Three cards are drawn successively with replacement from a well - shuffled pack of 52 cards. Find the mean and variance of some red cards.

Students Store