Let's begin by listing the first few multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 38, 40, 44. So, between 1 and 37 there are 9 such multiples: {4, 8, 12, 16, 20, 24, 28, 32, 36}. Note that 4 divided into 36 is 9.
Let's experiment by modifying the given problem a bit, for the purpose of discovering any pattern that may exist:
<span>How many multiples of 4 are there in {n; 37< n <101}? We could list and then count them: {40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100}; there are 16 such multiples in that particular interval. Try subtracting 40 from 100; we get 60. Dividing 60 by 4, we get 15, which is 1 less than 16. So it seems that if we subtract 40 from 1000 and divide the result by 4, and then add 1, we get the number of multiples of 4 between 37 and 1001:
1000 -40 ------- 960
Dividing this by 4, we get 240. Adding 1, we get 241.
Finally, subtract 9 from 241: We get 232.
There are 232 multiples of 4 between 37 and 1001.
Can you think of a more straightforward method of determining this number? </span>
<h3>What is meant be mean and standard deviation?</h3>
The ratio of sum of observations to the total number of observation is known as mean. It is one of the central tendency in the statistics. It gives an idea about the central value present in the data. The most sensitive measure of central tendency is mean. It is very easy to calculate. Mean playa a crucial role in daily life. The two types of means are Arithmetic mean and Geometric mean.
Standard deviation is a measure in the statistics. The amount of variation of a set of values is known as standard deviation. Standard deviation is denoted by σ.
As per given data
90% confident level for amount of electricity used in community of Austin is
X-tx/2(n-1)s/√n < μ < X+ tx/2(n-1)s/√n
Here , n=12 , X=10681.07 , s=6893.87
Margin of error = tx/2(n-1)s/√n
=(1.796×6893.87)/√12
=3574.1996
=3574.19(approximately)
Therefore, 90% CI is,
10681.07-3574.19 ≤ μ<10681.07+3574.19
7106.87 < μ< 14255.27
To know more about mean and standard deviation, visit:
