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Answer:
A) 585 miles
B) 584 miles
Step-by-step explanation:
We are told that the satellite pass directly over two tracking stations A and B, which are 90 mi apart.
This means that we can look at this as forming a kind of triangle where Tracking stations A & B will be
opposite ends of the base of the triangle while the satellite position will be the apex of the triangle.
We are given the angles of elevation at A and B to be 87.0° and 84.2° respectively.
Now, if we depict the satellite position as C. Then we have;
Angle at C = 180 - (87 + 84.2)
Angle at C = 8.8°
I've attached an image depicting this triangle.
A) To find the distance of the satellite from Station A, from the image attached, the distance will be AC.
Since AB is 90 mi.
Thus, using sine rule, we have;
AB/sin C = AC/sinB
Plugging in the relevant values;
90/(Sin 8.8) = AC/(sin 84.2)
AC = (90 × (sin 84.2))/(Sin 8.8)
AC = 585.27
To the nearest mile gives;
AC = 585 miles
B) To find out how high the satellite is above the ground, is the perpendicular distance from point C to line AB
Let's call the point at which the line touches AB as D.
It means angle D is 90° and it means triangle ADC it's a right angled triangle where AC is the hypotenuse = 585 miles.
Thus, using Trigonometric ratios we can find CD
Sin(87) = CD/585
CD = (Sin 87) x 585
CD = 584.198 miles
Approximating to the nearest mile gives;
CD = 584 miles
The point estimate of the mean for the data set is 90 and the standard deviation is approximately 5.59 .
The value of the parameter in the sample is used to determine the point estimate of a population parameter.
a) In this issue, the mean is the parameter whose estimate we seek.
Sample numbers for this issue are 94, 85, 85, 94, and 92.
(Amount of units sold monthly).
The sample mean is calculated as follows: Since the sample mean is calculated as the sum of all observations in the sample divided by the total number of observations:
Mean = (94 + 85 + 85 + 94 + 92)/5 = 90.
b) The data set for the number of units sold are 94 80 85 94 92
Standard deviation is calculated using the formula:
here n= 5
x = 90
Substituting the values we get
Sₙ = 5.585..
Sₙ ≈ 5.59
Therefore the mean is a) 90 and the standard deviation is approximately 5.59 .
The standard deviation in statistics is a measure of variation or dispersion (which relates to the degree to which a distribution is stretched or compressed) between values in a set of data. It is typically represented by the symbol.
The tendency is that the lower the standard deviation, the closer the data points will be to the mean (or expected value). On the other side, a higher standard deviation indicates a wider range of values
To learn more about standard deviation visit:
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