Answer:

Step-by-step explanation:
a. Given p=0.15.
-The mean of a sampling proportion of n=5000 is calculated as:

-The standard deviation is calculated using the formula:

Hence, the sample mean is μ=750 and standard deviation is σ=0.0050
b. Given that p=0.15 and n=1000
#The mean of a sampling proportion of n=1000 is calculated as:

#-The standard deviation is calculated as follows:

Hence, the sample mean is μ=150 and standard deviation is σ=0.0113
c. For p=0.15 and n=500
#The mean is calculated as follows:

#The standard deviation of the sample proportion is calculated as:

Hence, the sample mean is μ=75 and standard deviation is σ=0.0160
Answer:
Yes, they are independent because P(Texas) ≈ 0.45 and P(Texas/brand A) ≈ 0.45.
Step-by-step explanation:
We are given that a taste test asks people from Texas and California which pasta they prefer, brand A or brand B. The table is given in the question.
A person is randomly selected from those tested.
And we have find that are being from Texas and preferring brand A independent events or not.
Firstly, we know that these two events will be independent when;
P(Texas) = P(Texas/brand A)
Now, P(Texas) =
=
≈ 0.45
Also, P(Texas/brand A) =
=
=
≈ 0.45
Therefore, being from Texas and preferring brand A are independent events because P(Texas) ≈ 0.45 and P(Texas/brand A) ≈ 0.45.
Answer:
no
Step-by-step explanation:
Answer:
Where
and 
Since the distribution for X is normal then the distribution for the sample mean is also normal and given by:



So then is appropiate use the normal distribution to find the probabilities for 
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". The letter
is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: 
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 
Since the distribution for X is normal then the distribution for the sample mean
is also normal and given by:



So then is appropiate use the normal distribution to find the probabilities for 