Answer:
Step-by-step explanation:
Given that Heights of 10-year-olds, regardless of gender, closely follow a normal distribution with a mean of 55 inches and a standard deviation of 6 inches.
If X is height then X is N(55,6)
Z score would be 

b) 
c) Tallest 10% z = 1.28
X score =
inches
d)
i.e. 16.37% cannot go on this ride.
The outlier (61) is at the low end of the data set, but doesn't affect the mean by a lot, so ...
The mean is centered among the other numbers in both sets of data.
_____
The mean without the outlier is 114. With the outlier, it is 107.4. The lower quartile is 108, so the mean does get moved outside the "box" of the box-and-whisker plot of the data set without the outlier.
x = 12 , y = 18 (12, 18) is the solution, intersection of the two lines.
Answer : d. 438.5 ft
The diagram for the given statement is attached below.
Two sides AB and AC are equal so the angle B = angle C
WE know sum of three sides of a triangle = 180
angle A + angle B + angle C = 180
55 + B + C = 180
B + C = 180 -55 = 125
B and C are equal so we divide 125 by 2
angle B = 62.5 and angle C = 62.5
Now we apply sin law


150 * sin(55) = sin(62.5) * a
122.8728066 = sin(62.5) * a
a = 
a= 138.52 feet
To find perimeter we add all the sides
150 + 150 + 138.52 = 438.52 feet