Answer:
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
Where
and
And for this case we select a sample size of n= 81. Since the distribution for X is normal then we know that the distribution for the sample mean
is given by:
And the standard error of the mean would be:

4.1.5
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
Where
and
And for this case we select a sample size of n= 81. Since the distribution for X is normal then we know that the distribution for the sample mean
is given by:
And the standard error of the mean would be:

4.1.5
Answer:
Measured and Counted.
Step-by-step explanation:
Continuous data are usually “Measured”, but discrete data are usually “Counted”.
The continuous data are the data that can be measured, for example, Height of children, time in the race, length of leaf, etc. In this case, the data is taken within the range. While the discrete data is the data that can be counted. For example, the number of employees in the office, the number of students in the school, the result of rolling dice, etc. In this case, the data is a fixed number. Accordingly, the continuous data is measurable and discrete data is countable.
Answer:
9 is the number
Step-by-step explanation:
Let's call this number x
The equation is:
30+2x=48
subtract 30 from both sides and you get
2x=18
divide 2 from both sides and you get
x=9
Therefore, 30+2(9)=48