##### Question

In: Statistics and Probability

# A full-service car wash has an automated exterior conveyor car wash system that does the initial...

A full-service car wash has an automated exterior conveyor car wash system that does the initial cleaning in a few minutes. However, once the car is through the system, car wash workers hand clean the inside and the outside of the car for approximately 15 to 25 additional minutes. There are enough workers to handle four cars at once during this stage. On a busy day with good weather, the car wash can handle up to 150 cars in a 12-hour time period. However, on rainy days or on certain days of the year, business is slow. Suppose 50 days of work are randomly sampled from the car wash’s records and the number of cars washed each day is recorded. A stem-and-leaf plot of this output is constructed and is given below. Study the plot and write a few sentences describing the number of cars washed per day over this period of work. Note that the stem-and-leaf display is from Minitab, the stems are in the middle column, each leaf is only one digit and is shown in the right column, and the numbers in the left column are cumulative frequencies up to the median and then decumulative thereafter.

STEM-AND-LEAF DISPLAY: CARS WASHED PER DAY
Stem-and-leaf of Cars Washed Per Day N = 50 Leaf Unit = 1.0
 Stem Leaf 3 2 399 9 3 144778 15 4 015689 18 5 378 21 6 223 24 7 457 (3) 8 112 23 9 05 21 10 1234578 14 11 466 11 12 01467 6 13 37 4 14 1457

From the stem and leaf display, the original raw data can be obtained. For example, the fewest number of cars washed on any given day are ____. The most cars washed on any given day are _____. The modal stems are 3, 4, and 10 in which there are ___ days with each of these numbers. Studying the left column of the Minitab output, it is evident that the median number of cars washed is ____. There are only ___ days in which 90 some cars are washed (90 and 95) and only _____ days in which 130 some cars are washed (133 and 137).

## Solutions

##### Expert Solution

The first number 2|3 in the stem plot is the lowest number of cars washed per day and the last number 14|7 is highest number of cars washed per day.

Therefore, the fewest numb of cars washed on any given day are 23and The most cars washed on any given day are 147.

The modal stem 3 has frequency 6 days , the modal stem 4 has frequency of 6 days and the modal stem 10 has frequency 7 days .

Therefore, the modal stems are 3,4,10 in which there are 6+6+7=19 with each of these numbers.

Median is middle most number in the data set, there are total 50 days data set therefore median would be the average of 25th and 26th observation in the given stem plot.

25th number is 81 and 26 the number is also 81 , therefore the median is (81+81)/2 = 81.

Therefore, it is evidence that the median number of cars washed is 81 .

There are only 2 days (90 and 95) in which 90 some cars are washed and only 2 days ( 133 and 137) in which 130 some car are washed.

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