Approximately 10.3% of american high school students drop out of school before graduation. choose 10 students entering high scho
1 answer:
The probability that a binomial experiment of n trials and p, the probability of success, produces an outcome, x is given by:
Given that a<span>pproximately 10.3% of american high school students drop out of school before graduation, thus p = 0.103.
If we choose 10 students (i.e. n = 10)
The </span><span>probability that all 10 stay in school and graduate means the probability that none of the 10 students dropped out
is given by
</span>
Given that a<span>pproximately 10.3% of american high school students drop out of school before graduation, thus p = 0.103.
If we choose 10 students (i.e. n = 10)
The </span><span>probability that all 10 stay in school and graduate means the probability that none of the 10 students dropped out
</span>
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Answer:
The 95% confidence interval for the mean would be given by (56.604;68.596)
The 99% confidence interval for the mean would be given by (53.196;72.004)
Step-by-step explanation:
1) Previous concepts
When we compute a confidence interval for the mean, we are interested on the parameter population mean, and we use the info from the sample to estimate this parameter.
2) Basic operations
The sample mean can be calculated with the following formula
Using excel we can use this function to calculate the mean:
=AVERAGE(54.2,59.8,61.8,63.3,65.1,71.4)
The value obtained is
In order to find the sample deviation we can use this formula
And using excel we can use this function to calculate the sample standard deviation:
=STDEV.S(54.2,59.8,61.8,63.3,65.1,71.4)
The value obtained is
The sample size for this case is n=6, n<30 so then is better use the t distribution to calculate the margin of error. First we need to calculate the degrees of freedom, on this case
The formula for the confidence interval would be given by:
(1)
3) Part a
If we want a 95% or 0.95 of confidence, then the value for the signficance is , and
, and
so we can find the critical t value with the following formula in excel:
=T.INV(0.975,5)
And we got
And we can replace into equation (1) and we got:
And using excel with the following formulas we got:
=62.6-2.571*(5.713/SQRT(6)) = 56.604
=62.6+2.571*(5.713/SQRT(6)) = 68.596
So the 95% confidence interval for the mean would be given by (56.604;68.596)
4) Part b
If we want a 99% or 0.99 of confidence, then the value for the signficance is , and
, and
so we can find the critical t value with the following formula in excel:
=T.INV(0.995,5)
And we got
And we can replace into equation (1) and we got:
And using excel with the following formulas we got:
=62.6-4.032*(5.713/SQRT(6)) = 53.196
=62.6+4.032*(5.713/SQRT(6)) = 72.004
So the 99% confidence interval for the mean would be given by (53.196;72.004)
Answer:
The polynomial is an approximation with an error less than or equals to <em>0.002652</em> for x in the interval
[-1.113826815, 1.113826815]
Step-by-step explanation:
According to Taylor's theorem
with
for some c in the interval (-x, x)
In the particular case f
<em>f(x)=cos(x) </em>
<em> </em>
we have
therefore
and the polynomial approximation of T5(x) of cos(x) would be
In order to find all the values of x for which this approximation is within 0.002652 of the right answer, we notice that
for some c in (-x,x). So
and we must find the values of x for which
Working this inequality out, we find
Therefore the polynomial is an approximation with an error less than or equals to 0.002652 for x in the interval
[-1.113826815, 1.113826815]