Question

Use technology or a z-distribution table to find the indicated area. suppose the distances from the center of a target that arrows strikes are normally distributed with a mean of 20 cm and a standard deviation of 6.4 cm. approximately 25% of the arrows are further than what distance from the center?

Answer 1

Answer:

The correct answer is 24.3

Source: Just took the quiz

Answer 2

The answer is 12.64 cm.

We work backward from the probability given to us.  We look this probability up in a z-table (http://www.z-table.com).  Since it does not imply directionality, the score could be above or below the mean distance from center.  We divide 25%, 0.25, by 2 and get 0.125.  We look up 0.125 in the z-table and find that the score associated with it is -1.15.

The formula for a z-score is z=(X-μ)/σ.  Substituting our known information we have

-1.15 = (X-20)/6.4

Cancel the 6.4 by multiplying both sides:

-1.15(6.4) = (X-20)/6.4 * 6.4
-7.36 = X - 20

Now add 20 to both sides:

-7.36 + 20 = X - 20 + 20
12.64 = X.