Erica makes 4,840$ monthly. What is the maximum loan she can take out on a house?
1 answer:
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Answer:
a)
And we can find this probability with this difference and with the normal standard table or excel:
b)
And we can use the z score defined by:
And using the limits we got:
And we want to find this probability:
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".
Part a
Let X the random variable that represent the resitances 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 with this difference and with the normal standard table or excel:
Part b
We select a sample size of n =4. And since the distribution for X is normal then we know that the distribution for the sample mean is given by:
And we want this probability:
And we can use the z score defined by:
And using the limits we got:
And we want to find this probability:
Answer:
Length = 2.823 in (to 3 decimal places)
Step-by-step explanation:
assuming that the box is a cubic box:
volume of box = in³ = 22.5 in³
volume = Length × Length × Length = (Length)³
∴ (Length)³ = 22.5
∴ Length = ∛(22.5)
using the calculator punch ∛(22.5), and the answer is:
∴ Length = 2.823 in (to 3 decimal places)