Answer:
3. Standard deviation is the square root of the variance.
4. Standard deviation is useful because it has the same units as the underlying data.
Step-by-step explanation:
3. In statistics, the dispersion in a given data with respect to its mean distribution can be determined or measured by standard deviation and variance. The standard deviation of a distribution can also be determined as the square root of variance.
4. Standard deviation is measured in the same units as that of the original data. Thus it has the same units as the underlying data.
Answer:
The condition are
The Null hypothesis is 
The Alternative hypothesis is
The check revealed that
There is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons
Step-by-step explanation:
From the question we are told that
The population mean is 
The sample size is n = 20
The sample mean is 
The standard deviation is 
The Null hypothesis is 
The Alternative hypothesis is
So i will be making use of
level of significance to test this claim
The critical value of
from the normal distribution table is 
Generally the test statistics is mathematically evaluated as

substituting values


Looking at the value of t and
we see that
so we fail to reject the null hypothesis
This implies that there is sufficient evidence to support the claim that in a small city renowned for its music school, the average child takes at least 5 years of piano lessons.
Answer:
Step-by-step explanation:
How to write numbers in standard form:
Write the first number 8.
Add a decimal point after it: 8.
Now count the number of digits after 8. There are 13 digits.
So, in standard form: 81 900 000 000 000 is 8.19 × 10¹³
ANSWER

EXPLANATION
We can use any two points to determine the slope.
The line passes through;
(-3,1) and (-5,5).
The slope is given by

This implies that;


We can now find the equation using the formula;


Expand:

