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2 answers:
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Hello!
Let's write some important information contained in the exercise:
• hotdogs: $2.59 (,x,)
,• hamburgers: $5.29 (,y,)
He needs 11 packages. Let's write it:
• x + y = 11
He spent a total of $39.29. We can write it as:
• 2.59x + 5.29y = 39.29
Now, let's solve these two equations as a linear system:
First, let's isolate x in equation A:
Now, we will replace where's x by 11-y in equation B:
As I called the hamburgers as 'y', we know that he bought 4 packages of hamburgers.
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.