Question

A quality control analyst collected 200 measurements of length.The range of the 200 measurements is 17 cm.and one of the measurements is 49.5 cm.

Which of the following could be another one of the 200 measurements.
a)31
b)32
c)33
d)34

Answer 1

With a range of 17 cm and a known measurement of 49.5 cm, the possible range of the data set is between 32.5 cm and 66.5 cm. Therefore, answers (b) 32, (c) 33, and (d) 34 could all be correct as they fall within the determined range.

Step-by-step explanation:

The question relates to the concept of range in statistics, which is the difference between the highest and lowest values in a set of data. In this case, we know the range of 200 measurements is 17 cm, and one of the known measurements is 49.5 cm. To determine which of the options (a) 31, (b) 32, (c) 33, (d) 34 could also be a measurement in this set, we need to find the highest and lowest possible values that can be achieved with a range of 17 cm.

Considering a measurement of 49.5 cm is already known, the lowest possible value would be 49.5 cm - 17 cm = 32.5 cm, and the highest possible value would be 49.5 cm + 17 cm = 66.5 cm. Any other measurement within this dataset must fall within this range.

Among the provided options, (a) 31 is lower than 32.5 cm, so it cannot be in the range. Options (b) 32, (c) 33, and (d) 34 all fall within the 32.5 cm to 66.5 cm range. Therefore, any of these could be another one of the 200 measurements. Since you must choose one, without additional data, each of these options is equally likely to be a measurement in the dataset.

Answer 2

Given the range of 17 cm and a measurement of 49.5 cm, we find that another measurement could be 33 cm since it falls within the calculated range of possible measurements. The other options either fall outside this range or, while they fall inside the range, are not the smallest value greater than 32.5 (the calculated minimum value).

Step-by-step explanation:

The question is asking us to determine which among the provided options could be another measurement out of the 200 measurements taken, given that the range is 17 cm and one of the measurements is 49.5 cm. Since the range is the difference between the maximum and minimum values in a set, if we take 49.5 cm as either the maximum or minimum value, we can calculate the other value in that range by either adding or subtracting 17 cm from 49.5 cm. If 49.5 cm were the maximum value, the minimum would be 49.5 cm - 17 cm = 32.5 cm. If 49.5 cm were the minimum, the maximum would be 49.5 cm + 17 cm = 66.5 cm.

So the measurements would fall between 32.5 cm and 49.5 cm (if 49.5 is the maximum) or between 49.5 cm and 66.5 cm (if 49.5 is the minimum). Therefore, the values less than 49.5 cm but no less than 32.5 cm could be part of the 200 measurements. Looking at the options provided:

• 31 cm is outside the possible range if we consider 49.5 as max, so it cannot be correct.
• 32 cm is also outside the range, so it cannot be correct.
• 33 cm is inside the possible range, so it could be a correct answer.
• 34 cm is also inside the range, so it could be correct as well.

However, since we are asked to pick one of the options, and option (a) 31 and (b) 32 cannot be correct, and while both (c) 33 and (d) 34 could be correct, the correct answer must be the one most limits of the range. That is, the smallest value greater than 32.5, which is (c) 33 cm.