How to solve and respond.
1 answer:
Step-by-step explanation:
the error:
it is stated that
subtract (5x)/(x+7) from both sides
multiply both sides by x + 7
7(x+7) = 49x
7x + 49 = 49x
subtract 7x from both sides to isolate x and its coefficient
49 = 42x
thus, this is only true when 49 = 42x. in order for these two equations to be equal, they must <em>always </em>be true, so this is wrong
the solution:
we want to express 7/x as (something) / (x+7). to do this, we can multiply 7/x by 1.
anything divided by itself = 1. thus, if we multiply both the numerator and the denominator by something that turns x into (x+7), we can do what we want to do.
(x+7)/x * x turns x into (x+7), so we multiply both the numerator and denominator by (x+7)/x to get
substitute this for 7/x in our original problem
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Answer:
a)
b)
c)
Step-by-step explanation:
1) 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".
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
2) Part a
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where and
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 on this way:
3) Part b
From the central limit theorem we know that the distribution for the sample mean is given by:
And using a calculator, excel or the normal standard table we have that:
4) Part c
And using a calculator, excel or the normal standard table we have that: