Question

The owner of an auto repair shop studied the waiting times for customers who arrive at the shop for an oil change. The following data with waiting times in minutes were collected over 1-month.

2; 5; 10; 12; 4; 4; 5; 17; 11; 8; 9; 8; 12; 21; 6; 8; 7; 13; 18; 3
Using classes of 0-4, 5-9, and so on, construct:
a. The frequency distribution.
b. The relative frequency distribution.
c. The cumulative frequency distribution.
d. The proportion of customers needing an oil change who wait 9 minutes or less.

Answer 1

(d)0.6

Explanation:

(a)Frequency Distribution

`\left|\begin{array}c$Waiting Time(in Minutes)&$Frequency\\-----------&--\\0-4&4\\5-9&8\\10-14&5\\15-19&2\\20-24&1\\--&--\\Total&20\end{array}\right|`

(b)The relative frequency distribution.

`\left|\begin{array}c$Waiting Time(in Minutes)&$Relative Frequency\\-----------&--\\0-4&4/20=0.2\\5-9&8/20=0.4\\10-14&5/20=0.25\\15-19&2/20=0.1\\20-24&1/20=0.05\\--&--\\Total&1\end{array}\right|`

(c)The cumulative frequency distribution.

`\left|\begin{array}c$Waiting Time(in Minutes)&$Frequency&$Cumulative Frequency\\-----------&--&---\\0-4&4&4\\5-9&8&12\\10-14&5&17\\15-19&2&19\\20-24&1&20\\--&--&--\\Total&20\end{array}\right|`

(d)The proportion of customers needing an oil change who wait 9 minutes or less.

Proportion of customers needing an oil change who wait 9 minutes or less.

`=(12)/(20) \\\\=0.6`