Is this answer correct?
1 answer:
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Answer:
a) 0.7486; b) 0.6518; c) No
Step-by-step explanation:
We use z scores to answer these questions. The formula for a z score is
Our mean, μ, is 44; our standard deviation, σ, is 1.5.
For part a,
We want P(X > 43):
z = (43-44)/1.5 = -1/1.5 = -0.67
Using a z table, we see that the area under the curve to the left of this is 0.2514. However, we want the area to the right; this means we subtract from 1:
1 - 0.2514 = 0.7486
For part b,
We want P(42 ≤ X ≤ 45):
z = (42-44)/1.5 = -2/1.5 = -1.3
z = (45-44)/1.5 = 1/1.5 = 0.67
Using a z table, the area under the curve to the left of z = -1.3 is 0.0968. The area under the curve to the left of z = 0.67 is 0.7486.
The area between them is 0.7486 - 0.0968 = 0.6518.
For part c,
A response of 35 has a z score of
z = (35-44)/1.5 = -9/1.5 = -6
This is 6 standard deviations below the mean. This is more than the amount required to make this an outlier, or an unlikely response.
Let's suppose we want to solve 
with 
. Separating variables and integrating, we get
Leaving the solution in this form, the initial condition gives
This means the solution is
.
Now if we were to write
, then we would have found
so that the solution would have been
.
But these two solutions are the same, since
. So we get the same solution regardless of where we place 
, despite getting different values for .
Leaving the solution in this form, the initial condition gives
This means the solution is
Now if we were to write
so that the solution would have been
But these two solutions are the same, since