Find the 34th percentile, p34, from the following data 13.6, 14.3, 15.4, 15.7, 16.8, 23.1, 25.8, 26.3, 26.4, 26.7, 29.6, 39.8, 42.7, 43.4, 43.5, 45.8, 47, 47.1, 48.4, 49.7,

25.8

Step-by-step explanation:

The given data set is

13.6, 14.3, 15.4, 15.7, 16.8, 23.1, 25.8, 26.3, 26.4, 26.7, 29.6, 39.8, 42.7, 43.4, 43.5, 45.8, 47, 47.1, 48.4, 49.7

We need to find the 34th percentile for the given data set.

The given data already arranged in ascending order.

Now, compute the position of the pth percentile (index i).

It is given that p = 34 and n = 20

The index 6.8 is not an integer, round up. So,

i ≈ 7

It means the number at 7th position is the 34th percentile, i.e., 25.8 .

Therefore, the 34th percentile is 25.8.

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step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

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