The upper boundaries for a distribution of waiting times (in seconds) in a grocery store aisle are 46, 59, 72, and 85. List the value for each lower boundary in this distribution.

Lower boundary of 46 = 33

Lower boundary of 59 = 47

Lower boundary of 72 = 60

Lower boundary of 85 = 73

Step-by-step explanation:

Since the difference between each of the two successive numbers is 13. This implies that the difference between the upper and the lower boundaries for each of the class is 12.

Therefore, we have to subtract 12 from each of the upper boundary given the question to obtain their lower boundary as follow:  

Lower boundary of 46 = 46 - 12 = 33

Lower boundary of 59 = 59 - 12 = 47

Lower boundary of 72 = 72 - 12 = 60

Lower boundary of 85 = 85 - 12 = 73

Note:

It can be observed that the lower boundary of each upper can also be obtained by adding 1 to the immediate previous upper boundary. But, we adopt the above method in order to get the lower boundary of 46 since there is immediate previous upper boundary for 33 that is included in the question. With the method used above, one get as many lower and upper boundaries as one wants.

hello :

by applying the distributive property :

6 × 4.3 = 6 × ( 4 + 0.3 )

            =   (6 ×   4) + (6 ×   0.3)

            = 24 + 1.8

6 × 4.3 = 25.8