Answer:
And we can find this probability using the complement rule:
And using the normal standard distirbution table or excel we got:
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".
Solution to the problem
Let X the random variable that represent the variable if interest of a population, and for this case we know the distribution for X is given by:
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability using the complement rule:
And using the normal standard distirbution table or excel we got:
6m+2/=37×8
6m=296-2
6m=294
m=49
I assume you meant to type x for %.
If not, basically back-substitute at the end of the solution.
F(x) = 4x - 3
Let y = F(x)
y = 4x - 3
x = 4y - 3
x - 3 = 4y
(x - 3)/4 = y
Let y = F^(-1)x
F^(-1)x = (x - 3)/4
If you want % in your answer, just replace x for % in your answer.
Answer:
The average number of trials required to get the first success
Answer:
We need a sample size of at least 75.
Step-by-step explanation:
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
.
So it is z with a pvalue of
, so 
Now, we 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 standard deviation is the square root of the variance. So:

With a .95 probability, the sample size that needs to be taken if the desired margin of error is 5 or less is
We need a sample size of at least n, in which n is found when M = 5. So







We need a sample size of at least 75.