6 pints of a 20 percent solution of alcohol in water are mixed with 4 pints of a 10 percent alcohol in water solution. The perce
2 answers:
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Answer:
A. Normal
B. Between 40.08 minutes and 43.92 minutes.
C. About 95 percent of these confidence intervals will contain the true population mean number of minutes of concentration and about 5 percent will not contain the true population mean number of minutes of concentration.
Step-by-step explanation:
Central Limit Theorem
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 a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation
x% confidence interval:
A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.
Question A:
By the Central Limit Theorem, a normal distribution.
Question B:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
That is z with a pvalue of , so Z = 1.96.
Now, find the margin of error M as such
In which is the standard deviation of the population and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 42 - 1.92 = 40.08 minutes
The upper end of the interval is the sample mean added to M. So it is 42 + 1.92 = 43.92 minutes
Between 40.08 minutes and 43.92 minutes.
Question C:
x% confidence interval -> x% will contain the true population mean, (100-x)% wont.
So, 95% confidence interval:
About 95 percent of these confidence intervals will contain the true population mean number of minutes of concentration and about 5 percent will not contain the true population mean number of minutes of concentration.
Answer:
Option C. Anna and Sara
Step-by-step explanation:
<u><em>The complete question in the attached figure</em></u>
Let
h ----> the minimum height h in inches necessary to ride a certain roller coaster
we have
The solution for this inequality is the interval [48,∞)
so
The value of h must be greater than or equal to 48 inches
<u><em>Verify who can ride the roller coaster</em></u>
1) Miguel 42 in
substitute the value of h in the inequality
----> is not true
therefore
Miguel can't ride the roller coaster
2) Patrick 45 in
substitute the value of h in the inequality
----> is not true
therefore
Patrick can't ride the roller coaster
3) Anna 48 in
substitute the value of h in the inequality
----> is true
therefore
Anna can ride the roller coaster
4) Sara 52 in
substitute the value of h in the inequality
----> is true
therefore
Sara can ride the roller coaster
