Question

Mann, Introductory Statistics, 9e Help I System Announcements Grace Period: 4 days left I Register No PRINTER VERSION BACK NEXT 8th-ed Chap 02, Sec 2.3, Problem 035 The following table gives the frequency distribution of the number of days to expiry date for all containers of yogurt in stock at a local grocery store. Containers that had already expired but were still on the shelves were given a value of 0 for number of days to expiry date. Number of Days 0 to 5 6 to 11 12 to 17 18 to 23 24 to 29 Number of Containers 31 68 45 20 10 b. Calculate the cumulative relative frequency and cumulative percentage for each class. Round your answers for relative frequencies to three decimal places and your answers for percentages to one decimal place. mber of Days Cumulative Frequency Cumulative Relative Frequency 0 to 5 0 to 11 0 to 17 0 to 23 0 to 29 SHOW HINT c. Find the percentage of the containers that will expire in 12 or more days. Round your answer to one decimal place. the tolerance is +/-2%

Answer 1

a) The table below gives the required cumulative frequency distribution for the number days to expire for the containers at the grocery store. The calculation is shown in the table itself.

b) For calculating the cumulative relative frequencies, we need to first calculate the relative frequencies for each class. Relative frequency is calculated as:

   $Relative frequency = \frac{Frequency \hspace{.1cm} of \hspace{.1cm} a \hspace{.1cm} given \hspace{.1cm} class}{Sum \hspace{.1cm} of \hspace{.1cm} all \hspace{.1cm} frequencies}$

The sum of all frequencies is = 31+68+45+20+10 = 174.

The cumulative relative frequencies are calculated by taking the sum of all relative frequencies preceding that class. The computation is shown in the table.

The cumulative percentages are calculated by multiplying each cumulative relative frequency by 100. Another way of calculating the cumulative percentage is given by the formula:

   $Cumulative \hspace{.1cm} percentage = \frac{Cumulative \hspace{.1cm} frequency \hspace{.1cm} of \hspace{.1cm} a \hspace{.1cm} class}{Sum \hspace{.1cm} of \hspace{.1cm} all \hspace{.1cm} frequencies}*100$

No. of days	Cumulative Frequency	Relative frequency	Cumulative relative frequency	Cumulative percentage
0-5	31	0.178	0.178	17.8
0-11	31+68 = 99	0.391	0.178+0.391 = 0.569	56.9
0-17	99+45 = 144	0.259	0.569+0.259 = 0.828	82.8
0-23	144+20 = 164	0.115	0.828+0.115 = 0.943	94.3
0-29	164+10 = 174	0.057	0.943+0.057 = 1	100

c) The number of containers that will expire in 12 or more days is obtained by adding the number of containers in the classes 12-17, 18-23, and 24-29, i.e., 45+20+10 = 75.

   $The \hspace{.1cm} required \hspace{.1cm} percentage = \frac{75}{174}*100 = 43.1\%$