Eighty-five more than the square of a number is the same as the square of the quantity that is 17 less than the number. What is
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Answer:
99.27% probability that among 6 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.
Step-by-step explanation:
For each student, there are only two possible outcomes. Either they find a job in their chosen field within one year of graduating, or they do not. The probability of a student finding a job in their chosen field within one year of graduating is independent of other students. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
56% of the school's graduates find a job in their chosen field within a year after graduation.
This means that
Find the probability that among 6 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.
This is when n = 6.
Either none find a job, or at least one does. The sum of the probabilities of these events is decimal 1. So
In which
99.27% probability that among 6 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.
Consequently, t<span>he limit of
In other words,
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so oblique asymptote is y=x.
I'm Japanese, if you find some mistakes in my English, please let me know.</span>
Answer:
a)
b) The 95% confidence interval would be given by (138.846;149.754)
c) n=34
d) n=298
e) n=1190
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
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".
We can calculate the sample mean with this formula:
represent the sample mean
population mean (variable of interest)
represent the population standard deviation
n=10 represent the sample size
a) Find a point estimate of the population mean
We can calculate the sample mean with this formula:
b) Construct a 95% confidence interval for the true mean score for this population.
The confidence interval for the mean is given by the following formula:
(1)
Since the Confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by (138.846;149.754)
Part c
The margin of error is given by this formula:
(a)
And on this case we have that ME =+20 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got , replacing into formula (5) we got:
So the answer for this case would be n=34 rounded up to the nearest integer
Part d
So the answer for this case would be n=298 rounded up to the nearest integer
Part e
So the answer for this case would be n=1190 rounded up to the nearest integer