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Home KPK NOTES BISE Swat Statistics Class 11

Statistics Chapter 8 (Hypergeometric and binomial Probability Distribution)

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Hypergeometric and binomial Probability Distribution
Hypergeometric and binomial Probability Distribution

(Hypergeometric and binomial Probability Distribution) Chapter 8

Table of Contents

  • (Hypergeometric and binomial Probability Distribution) Chapter 8
  • Q.2) Define Bernoulli’s probability distribution.
  • Q.3) If 5 cards are dealt from a standard deck of 52 playing cards what is the probability that 3 will be clubs.
  • Q.4) Prove that mean and variance of Bernoulli distribution is p and pq.
  • Q.9) Find the probabilities of the binomial experiment defined by n = 6 and p = 0.5.
  • Q.11) If 30% of a population on their own homes, wheat is the probability that a sample of seven from the population will contain:
  • Q.12) If the probability of getting defective items in a lot containing 200 items is 0.2, find the expected number of defective items in the lot and find its standard deviation.
  • Q.13) The output of a production process is 10% defective. What is the probability of selecting exactly two defectives in a sample of five?

Q.1 a). The telephone company reports that among 5000 telephones installed in a new subdivision 4000 have push buttons. If 10 people are called at random what is the probability that exactly 3 will be talking on dial telephones?
b). Define hypergeometric distribution.

Answer:
a) Let X denote the number of people that have dial telephones. probability of a push-button telephone is

Statistics Chapter 8 (Hypergeometric and binomial Probability Distribution) 17

b) HYPERGEOMETRIC DISTRIBUTION:
A probability distribution used to predict the outcome of a process in which different elements are randomly drawn from a collection and not replaced. For example, a hypergeometric distribution could be used to predict what color marble would be drawn from a jar if each marble drawn is not replaced.
FORMULA:

FORMULA
Statistics Chapter 8 (Hypergeometric and binomial Probability Distribution) 18

Q.2) Define Bernoulli’s probability distribution.

Answer:
BERNOULLI DISTRIBUTION:
An experiment in which a single action, such as flipping a coin, is repeated identically repeatedly. The possible results of the action are classified as “success” or “failure”. The binomial probability formula is used to find probabilities for Bernoulli trials.

this
Statistics Chapter 8 (Hypergeometric and binomial Probability Distribution) 19

In probability theory and statistics, the Bernoulli distribution, named after Swiss scientist Jacob Bernoulli, 1: is the probability of a random variable, which takes the value 1 with success probability of  P and the value 0 with failure probability of q=i-p . It can be used to represent a coin toss where 1 and 0 would represent “head” and “tail” (or vice versa), respectively. In particular, unfair coins would have  P  is not equal to 0.5.
The Bernoulli distribution is a special case of the two-point distribution, for which the two possible outcomes need not be 0 and 1.

Q.3) If 5 cards are dealt from a standard deck of 52 playing cards what is the probability that 3 will be clubs.

Answer:

Related: Statistics Chapter 7 (RandomVariable and Probability Distribution)

cards
Statistics Chapter 8 (Hypergeometric and binomial Probability Distribution) 20

Q.4) Prove that mean and variance of Bernoulli distribution is p and pq.

Answer:

the mean
Statistics Chapter 8 (Hypergeometric and binomial Probability Distribution) 21

Q.6) The mean and variance of binomial distribution are 3 and 2, respectively. Find the probability that the variate takes values
i) less than or equal to 2
ii) greater than or equal to 7.

Related: Statistics Chapter 6 (Probability) | Class 11 for KPK

greater than
Statistics Chapter 8 (Hypergeometric and binomial Probability Distribution) 22

Q.9) Find the probabilities of the binomial experiment defined by n = 6 and p = 0.5.

Related: Statistics Chapter 5 (Index number)

pa
Statistics Chapter 8 (Hypergeometric and binomial Probability Distribution) 23
paaa
Statistics Chapter 8 (Hypergeometric and binomial Probability Distribution) 24

Q.10) The probability of a man scoring a penalty in a Hockey match is 1/3. How many times he should be given a chance so that the probability of scoring successfully at least once is greater than ¾?

Related: Statistics – Chapter 4 (Measure of Dispersion)

didi

Q.11) If 30% of a population on their own homes, wheat is the probability that a sample of seven from the population will contain:

a) Exactly two homeowners?
b) At least five homeowners?
c) Exactly four homeowners?

Answer:

Statistics Chapter 8 (Hypergeometric and binomial Probability Distribution) 25

Statistics Chapter 8 (Hypergeometric and binomial Probability Distribution) 26

Q.12) If the probability of getting defective items in a lot containing 200 items is 0.2, find the expected number of defective items in the lot and find its standard deviation.

Answer:

anss
Statistics Chapter 8 (Hypergeometric and binomial Probability Distribution) 27

Q.13) The output of a production process is 10% defective. What is the probability of selecting exactly two defectives in a sample of five?

Answer:

Read more: Statistics-Chapter 3 (Measures of Location)

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pakk
Statistics Chapter 8 (Hypergeometric and binomial Probability Distribution) 28

Q.14 a) Compute the mean and standard deviation for the binomial distribution for which p = 0.7 and n = 60.

b) Discuss the statement that is a binomial distribution n=5 and p=2.5.
c) The mean and variance of a binomial distribution are 42 and 12.6 respectively. Find p and n.
d) Is it possible to have binomial distribution with mean=5 and S.D=3?

Answer:

part 1
Statistics Chapter 8 (Hypergeometric and binomial Probability Distribution) 29

PART B:
Since p is greater than one so binomial distribution does not exist:

Related: Statistics Chapter 2 (Collection and presentation of Data) | Class 11 Notes

part b
Statistics Chapter 8 (Hypergeometric and binomial Probability Distribution) 30

Statistics Class 11 Notes Cha 1 (Introduction To Statistics)

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