A bank pays 7% interest on 3-year certificates of deposit. What is the value of a $500 certificate after one year? Give your ans
2 answers:
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Answer:
y = -1/2 + 2 (Slope intercept)
Step-by-step explanation:
Y-intercept is when the x-value is 0.
So the y-intercept is (0, 2)
To find slope, find two random points:
(0, 2) , (2, 1)
Slope (m) =ΔY/ΔX = -1/2 = -0.5
Equation of the line:
y = -0.5x + 2
or
y = -1/2 + 2
When x=0, y = 2
When y=0, x = 4
Answer:
A. 13.9 and 14.1 inches
See explanation below.
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 outside diameters of a population, and for this case we know the distribution for X is given by:
Where and
If we want the middle 68% of the data we need to have on the tails 16% on each one
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.16 of the area on the left and 0.84 of the area on the right it's z=-0.994. On this case P(Z<-0.994)=0.16 and P(z>-0.994)=0.84
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
And since the distribution is symmetrical for the upper limit we can use z = 0.994 and we have:
And if we solve for a we got
So the correct answer for this case would be:
A. 13.9 and 14.1 inches