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#4) From the reference angle of 58° we can see that we have the side opposite to that angle as well as the hypotenuse. Recall that sin=opp/hyp so we are going to use sine to find that side
sin(58°) =
(multiply both sides by 19 to isolate x)
19 sin(58°) = x (plug into calculator)
16.1 = x
#5) From the reference angle of 56°, we see that we have the adjacent and the opposite sides. Remember that tan=opp/adj so we will use tangent to find x
tan(56°) =
(multiply both sides by 
)
(flip them so x is on the top)
[tex] \frac{12}{tan(56)} = x
8.1 = x
sin(58°) =
19 sin(58°) = x (plug into calculator)
16.1 = x
#5) From the reference angle of 56°, we see that we have the adjacent and the opposite sides. Remember that tan=opp/adj so we will use tangent to find x
tan(56°) =
[tex] \frac{12}{tan(56)} = x
8.1 = x
Answer:
a) P(-z_0.025 < Z < z_0.025)
For this case we want a quantile that accumulates 0.025 of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:
"=NORM.INV(0.025,0,1)"
"=NORM.INV(0.025,0,1)"
And for this case the two values are :
b) P(-z_{\alpha/2} < Z < z_{\alpha/2})
For this case we want a quantile that accumulates of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:
"=NORM.INV(alpha/2,0,1)"
"=NORM.INV(alpha/2,0,1)"
c) For this case we want to find a value of z that satisfy:
P(Z > z_alpha) = 0.05.
And we can use the following excel code:
"=NORM.INV(0.95,0,1)"
And 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
Part a
P(-z_0.025 < Z < z_0.025)
For this case we want a quantile that accumulates 0.025 of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:
"=NORM.INV(0.025,0,1)"
"=NORM.INV(0.025,0,1)"
And for this case the two values are :
Part b
P(-z_{\alpha/2} < Z < z_{\alpha/2})
For this case we want a quantile that accumulates of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:
"=NORM.INV(alpha/2,0,1)"
"=NORM.INV(alpha/2,0,1)"
Part c
For this case we want to find a value of z that satisfy:
P(Z > z_alpha) = 0.05.
And we can use the following excel code:
"=NORM.INV(0.95,0,1)"
And we got