Solve the problem.
-A spinner has five regions numbered 1 through 5. If the spinner is spun 100 times, we would expect about 20 of the outcomes to be Region 1. It can be determined that the spinner is unbalanced if x, the number of outcomes that result in Region 1, satisfies $\left| \frac { x - 20 } { 4 } \right| \geq 1.645$. Describe the number of outcomes that determine an unbalanced spinner that is spun 100 times.
A) Fewer than 14 or more than 26 outcomes
B) Fewer than 17 or more than 29 outcomes
C) Between 14 and 26 outcomes
D) Between 17 and 29 outcomes

Question

Quizplus · Accepted Answer

Solving the inequality $\left| \frac { x - 20 } { 4 } \right| \geq 1.645$ gives us the range for x outside of which the spinner is considered unbalanced. Simplifying the inequality, we find that x must be either less than 13.42 or greater than 26.58. Since x represents the number of outcomes and must be an integer, the spinner is considered unbalanced if there are fewer than 14 or more than 26 outcomes of Region 1.

Solve the Problem ∣x−204∣≥1.645\left| \frac { x - 20 } { 4 } \right| \geq 1.645​4x−20​​≥1.645

Solve the Problem $\left| \frac { x - 20 } { 4 } \right| \geq 1.645$