Hi NupurNeha123,Happy to break this down step by step!
This question asks: what is the probability that the profit per unit falls WITHIN
$1 of the average? Let me walk you through the logic.
Step 1: Understand what 'within $1 of the average' means.If the average profit per unit is, say, $X, then 'within
$1 of the average' means the profit falls in the range from $(X -
1) to $(X +
1). So you need to identify ALL outcomes from the chart that fall inside this range.
Step 2: Read the chart carefully.The chart shows different profit-per-unit ranges (or outcomes) and their associated probabilities. You need to first locate the average profit per unit — this may be given directly or you may need to calculate it from the distribution shown.
Step 3: Identify which bars/ranges fall within $1 of that average.Once you know the average, look at the chart and find the ranges that overlap with the interval [average -
$1, average +
$1]. In this problem, exactly
TWO ranges from the chart fall within that
$1 window around the average.
Step 4: Add those two probabilities.The probability for one of those ranges is
0.1875 and the probability for the other is
0.125. Adding them gives:
0.1875 +
0.125 =
0.3125. This is the total probability of being within
$1 of the average.
Step 5: Match to the dropdowns.For D1, the
correct choice is 0.1875 (not
0.25 or
0.375). For D2, the
correct choice is 0.125 (not
0.5 or
0.0125). Together they complete the sentence: 'the probability... is equal to the sum of
0.1875 and
0.125.'
Key Insight: The
key trap here is reading the wrong bars from the chart or miscalculating which ranges fall inside the
$1 window. Make sure you are reading the profit values on the correct axis and matching them precisely to the average before selecting which probabilities to add.
Answer: 0.1875, 0.125