PSAT Math Grid-Ins Question 88: Answer and Explanation

Question: 88

The Kp Index measures the energy added to Earth's magnetic field from the Sun on a scale of 0–9, with 1 representing a solar calm and 5 or more indicating a magnetic storm, or solar flare. The magnetic fluctuations are measured in three-hour intervals (12 a.m.–3 a.m., 3 a.m.–6 a.m., and so on). The bar graph below shows the measurements for a five-day period in September.

If a single 3-hour time period between September 9 and September 13 (including the start and end dates) is chosen at random, what is the probability that a solar flare occurred during that time?

Correct Answer: 5/40 or 1/8 or .125

Explanation:

5/40 or 1/8 or .125

Difficulty: Medium

Category: Probability

Getting to the Answer: Probability compares the number of desired outcomes (number of 3-hour periods with a Kp index greater than or equal to 5) to the total number of possible outcomes (total number of 3-hour periods between September 9 and September 13).

Count the number of bars in the graph that have a height of 5 or more—there are 5. Count the total number of bars—there are 8 for each of the 5 days, for a total of 40. This means there were five 3-hour periods out of 40 during which a solar flare occurred, so the probability of randomly selecting one of those periods is . You could also grid in the answer as .125.