By the definition for the absolute value,


So for the compound function

, there are three intervals to consider. What happens when

? when

? when

?
You have
Answer:
The mean of the sampling distribution of the sample proportions is 0.82 and the standard deviation is 0.0256.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean
and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For proportions, the mean is
and the standard deviation is 
In this problem, we have that:
.
So


The mean of the sampling distribution of the sample proportions is 0.82 and the standard deviation is 0.0256.
Answer:
4/15
Step-by-step explanation:
40% is the same as .4.
.4 x 75 = 30
1/3 x 75 = 25
30 + 25 = 55
75 - 55 = 20
20 / 75
Simplify. Divide by 5.
4/15
Answer:
blue
Step-by-step explanation:
Its blue because if purple has 2 and blue has 1 then its blue which you are most likely to pick purple then blue