Answer:
42% of observations lie between 125 and 158.
Step-by-step explanation:
Interpretation of a percentile
When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x)% of the values in the set are higher than V.
Two values have a percentile, how many are between then?
In this example, y is larger than x.
When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x)% of the values in the set are higher than V.
When a value Z is said to be in the yth percentile of a set, y% of the values in the set are lower than V and (100-y)% of the values in the set are higher than V.
Also, (y-x)% of the values are between V and Z.
In this problem, we have that:
125 is the 40th percentile
158 is the 82nd percentile
Approximately what percentage of observations lie between 125 and 158
82 - 40 = 42% of observations lie between 125 and 158.
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