mathematics>Statistics>Probability Distributions>Fitting of Binomial, Poisson and Normal Distributions

Fitting of Binomial, Poisson and Normal Distributions

IMPORTANT

Fitting of Binomial, Poisson and Normal Distributions: Overview

This Topic covers sub-topics such as Fitting Binomial Distribution, Fitting Poisson Distribution and, Fitting Normal Distribution

Important Questions on Fitting of Binomial, Poisson and Normal Distributions

HARD

IMPORTANT

mathematics>Probability Distributions>Fitting of Binomial, Poisson and Normal Distributions> Q 1

A given set of $4$ coins are tossed $64$ times. The Number of occurrence of heads the table as given below

Number of Heads	$0$	$1$	$2$	$3$	$4$
Number of times	$3$	$15$	$23$	$17$	$6$

Then find a fitted Binomial distribution for the said data and find the expected frequencies for the given data.

HARD

IMPORTANT

mathematics>Probability Distributions>Fitting of Binomial, Poisson and Normal Distributions> Q 2

Fit a normal curve to the following data :

Class Intervals	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	Total
Frequency	$2$	$11$	$20$	$33$	$24$	$8$	$2$	$100$

HARD

IMPORTANT

mathematics>Probability Distributions>Fitting of Binomial, Poisson and Normal Distributions> Q 3

Fit a normal curve to the following data :

Class Intervals	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	Total
Frequency	$2$	$11$	$24$	$20$	$33$	$8$	$2$	$100$

HARD

IMPORTANT

mathematics>Probability Distributions>Fitting of Binomial, Poisson and Normal Distributions> Q 4

Fit a normal curve to the following data :

Class Intervals	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	Total
Frequency	$2$	$24$	$11$	$33$	$20$	$8$	$2$	$100$

HARD

IMPORTANT

mathematics>Probability Distributions>Fitting of Binomial, Poisson and Normal Distributions> Q 5

Fit a normal curve to the following data :

Class Intervals	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	Total
Frequency	$2$	$11$	$24$	$33$	$20$	$2$	$8$	$100$

HARD

IMPORTANT

mathematics>Probability Distributions>Fitting of Binomial, Poisson and Normal Distributions> Q 6

Fit a normal curve to the following data :

Class Intervals	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	Total
Frequency	$2$	$11$	$24$	$33$	$20$	$8$	$2$	$100$

MEDIUM

IMPORTANT

mathematics>Probability Distributions>Fitting of Binomial, Poisson and Normal Distributions> Q 7

A set of $4$ coins are tossed $64$ times. The Number of occurrence of heads is tabulated as follows

Number of Heads	$0$	$1$	$2$	$3$	$4$
Number of times	$3$	$23$	$17$	$15$	$6$

Fit a Binomial distribution for the above data and find the expected frequencies.

MEDIUM

IMPORTANT

mathematics>Probability Distributions>Fitting of Binomial, Poisson and Normal Distributions> Q 8

$4$ dice are thrown $200$ times. The frequencies for getting the numbers $4, 5$ or $6$ are tabulated as follows:

Getting $4, 5, 6$	$0$	$1$	$2$	$3$	$4$	Total
Frequency	$62$	$85$	$40$	$11$	$2$	$200$

Fit a Binomial distribution using the above data and estimate the expected frequencies for getting the numbers $4, 5$ or $6$

MEDIUM

IMPORTANT

mathematics>Probability Distributions>Fitting of Binomial, Poisson and Normal Distributions> Q 9

A set of $4$ coins are tossed $64$ times. The Number of occurrence of heads is tabulated as follows

Number of Heads	$0$	$1$	$2$	$3$	$4$
Number of times	$3$	$23$	$15$	$17$	$6$

Fit a Binomial distribution for the above data and find the expected frequencies.

MEDIUM

IMPORTANT

mathematics>Probability Distributions>Fitting of Binomial, Poisson and Normal Distributions> Q 10

A skilled typist on a routine work kept a record of mistake made per day during $300$ working days:

$\begin{array}{l} mistake/day & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ No. Falay & 143 & 90 & 42 & 12 & 9 & 3 & 1 \end{array}$

Fit a poisson distribution to the above given data.

MEDIUM

IMPORTANT

mathematics>Probability Distributions>Fitting of Binomial, Poisson and Normal Distributions> Q 11

Four hundred car air-conditioners are inspected as they come off the production line and the number of defects per set is recorded below

$\begin{array}{l} No. of defects : & 0 & 1 & 2 & 3 & 4 & 5 \\ No. of ACs: & 142 & 156 & 69 & 27 & 5 & 1 \end{array}$

Fit a poisson distribution to the above given data.

MEDIUM

IMPORTANT

mathematics>Probability Distributions>Fitting of Binomial, Poisson and Normal Distributions> Q 12

The number of defects per unit in a sample of $330$ units of manufactured product was found as follows:

$\begin{array}{l} No. of defects & 0 & 1 & 2 & 3 & 4 \\ No. of units & 214 & 92 & 20 & 3 & 1 \end{array}$

Fit a poisson distribution to the above given data.

HARD

IMPORTANT

mathematics>Probability Distributions>Fitting of Binomial, Poisson and Normal Distributions> Q 13

$100$ car radios are inspected as they come off from the production line and number of defects per set is recorded as below:

No. of defects	$0$	$1$	$2$	$3$	$4$
No. of sets	$79$	$18$	$2$	$1$	$0$

Fit a Poisson distribution and find the expected frequencies.

EASY

IMPORTANT

mathematics>Probability Distributions>Fitting of Binomial, Poisson and Normal Distributions> Q 14

Cotyledons are also called-