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Answer:
The length of the pole to the nearest feet = 36 ft
Step-by-step explanation:
Let the length of the pole be L
The image of this question is attached to this solution.
From the image,
The two other angles in the triangle formed by the stick, its shadow and the line of angle of elevation can be found.
The first angle to the right of angle of elevation = 90° - 8° = 82°
And the third angle can be found, using the sum of angles in a triangle.
Sum of angles in a triangle = 180°
The third angle = 180° - (70° + 82°) = 28°
Using the sine rule, we can then obtain the length of the pole.
Sine rule
(a/sin A) = (b/sin B) = (c/sin C)
For our question
(L/sin 70°) = (18/sin 28°)
L = (18 × sin 70°)/(sin 28°)
L = 36.03 ft = 36 ft
Answer:
a) 34.46% of 10-year-old boys is tall enough to ride this coaster.
b) 78.81% of 10-year-old boys is tall enough to ride this coaster
c) 44.35% of 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part a
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
a. What proportion of 10-year-old boys is tall enough to ride the coaster?
This is 1 subtracted by the pvalue of Z when X = 56.
So
has a pvalue of 0.6554
1 - 0.6554 = 0.3446
34.46% of 10-year-old boys is tall enough to ride this coaster.
b. A smaller coaster has a height requirement of 50 inches to ride. What proportion of 10-year-old boys is tall enough to ride this coaster?
This is 1 subtracted by the pvalue of Z when X = 50.
has a pvalue of 0.2119
1 - 0.2119 = 0.7881
78.81% of 10-year-old boys is tall enough to ride this coaster.
c. What proportion of 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part a?
Between 50 and 56 inches, which is the pvalue of Z when X = 56 subtracted by the pvalue of Z when X = 50.
From a), when X = 56, Z has a pvalue of 0.6554
From b), when X = 50, Z has a pvalue of 0.2119
0.6554 - 0.2119 = 0.4435
44.35% of 10-year-old boys is tall enough to ride the coaster in part b but not tall enough to ride the coaster in part a