EASY
Earn 100

X~Po42. Use the normal approximation to find: PX<50

Important Questions on The Normal Distribution

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Which of the following is not true regarding the normal distribution?

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The p. d. f. of a random variable x is given by fx=14a,a>00<x<4a,0,Otherwise and Px<3a2=kPx>5a2 then k=.
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If in a population of size ”N” the birth rate is represented as “b” and the death rate as “d”, the increase or decrease in “N” during a unit time period ”t” will be:

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The equation given above can also be represented as:

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What does ”r” represent. Write any one significance of calculating ”r” for any population? 

HARD
In Scotland, in November, on average 80% of days are cloudy. Assume that the weather on any one day is independent of the weather on other days.
Use a normal approximation to find the probability of there being fewer than 25 cloudy days in Scotland in November (30 days).
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Find the range, the three quartiles and the interquartile range for data represented by the following box-and-whisker plots.

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For each scatter plot, describe the form, direction and strength of the association between the variables. Interpret your description in the context of the data.

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The measure of resources enough to support a maximum possible number of species, beyond which no further growth is possible is known as 
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By first evaluating np and npq, use a suitable approximation and continuity correction to find PX<75 for the discrete random variable X~B100, 0.7.
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The intrinsic rate of natural increase is the sum of crude birth rate and crude death rate.
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For each scatter plot, describe the form, direction and strength of the association between the variables. Interpret your description in the context of the data.

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For each scatter plot, describe the form, direction and strength of the association between the variables. Interpret your description in the context of the data.

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EASY

Find the range, the three quartiles and the interquartile range for data represented by the following box-and-whisker plots.

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For each scatter plot, describe the form, direction and strength of the association between the variables. Interpret your description in the context of the data.

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The times of sunrise and of sunset in Reykjavik, Iceland, on the 1st of each month are represented in this table using hours and minutes.

Month(t) Rise set
0 11.20 15.42
1 10.09 17.13
2 8.37 18.43
3 6.47 20.16
4 5.01 21.49
5 3.24 23.27
6 3.05 23.57
7 4.34 22.34
8 6.09 20.47
9 7.35 19.00
10 9.09 17.13
11 10.44 15.49

Calculate the times in decimal notation. Explain why this is necessary.

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In 1981, the 'r' value for the human population in India was 0.0205.
Why is 'r' an important parameter?
HARD
The intrinsic rate of natural increase for Indian human population according to the 2011 census was
EASY

For each scatter plot, describe the form, direction and strength of the association between the variables. Interpret your description in the context of the data.

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EASY

Arable land is land that is used for growing crops. The amount of arable land can indicate how able a country is to produce food to support its citizens countries with the highest percentage of arable land (as a percentage of total land area) are listed in the table below.

Higher-income countries Lower-income countries
Denmark 58% Bangladesh 59%
Hungary 49% Ukraine 56%
Czech Republic 41% Moldova 55%
Isle of Man 39% India 53%
Lithuania 38% Togo 49%
Poland 36% Burundi 47%
Germany 34% Rwanda 47%
France 34% The Gambia 44%

Find the five-number summaries for the high and low income countries.Round to the nearest tenth where necessary.

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For each scatter plot, describe the form, direction and strength of the association between the variables. Interpret your description in the context of the data.

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Represent the union of two sets by Venn diagram for each of the following.

X={x | x is a prime number between 80 and 100}

Y={y | y is an odd number between 90 and 100}