Answer to Question #223417 in Statistics and Probability for Ratul

Question

The production manager wants to know the distribution of sizes among these 1500 shirts.

Monsoon Rain follows the following height chart for shirts:

Height Size

Less than 5 feet 4 inch small

5 feet 4 inch- 5 feet 8 inch Medium

5 feet 8 inch and above Large

t. The survey was done on 100 men ( age> 21). The data is given below;

Table: Heights observed from the sample.

SN Height (inch) SN Height (inch) SN Height (inch) SN Height (inch)

1 70 26 56 51 70 76 60

2 23 27 21 52 60 77 64

3 48 28 67 53 48 78 64

4 70 29 69 54 70 79 67

5 68 30 72 55 68 80 69

6 64 31 73 56 64 81 66

7 65 32 70 57 65 82 75

8 66 33 56 58 66 83 70

9 56 34 59 59 56 84 61

10 64 35 61 60 64 85 71

11 64 36 71 61 56 86 62

12 67 37 62 62 66 87 67

13 69 38 67 63 67 88 65

14 66 39 65 64 69 89 65

15 75 40 59 65 72 90 70

16 60 41 68 66 73 91 60

17 48 42 67 67 70 92 60

18 66 43 65 68 56 93 70

19 68 44 54 69 59 94 70

20 69 45 43 70 61 95 60

21 66 46 70 71 71 96 53

22 66 47 66 72 51 97 70

23 61 48 64 73 52 98 64

24 66 49 66 74 60 99 56

25 64 50 65 75 54 100 96

According to the above information, how many small, medium and large sized shirts should Monsoon rain produce to meet the market demand?

 

 

Answer 1

Solution:

First, let's arrange this data in ascending order:

21, 23, 43, 48, 48, 48, 51, 52, 53, 54, 54, 56, 56, 56, 56, 56, 56, 56, 59, 59, 59, 60, 60, 60, 60, 60, 60, 60, 61, 61, 61, 61, 62, 62, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 65, 65, 65, 65, 65, 65, 65, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 67, 67, 67, 67, 67, 67, 67, 68, 68, 68, 68, 69, 69, 69, 69, 69, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 70, 71, 71, 71, 72, 72, 73, 73, 75, 75, 96.

Less than 5 feet 4 inch small = (5x12+4) inch = Less than 64 inch

5 feet 4 inch- 5 feet 8 inch Medium = 64 inch - 68 inch Medium

5 feet 8 inch and above Large = 68 inch and above Large

No. of men having height less than 64 inch = 44

No. of men having height between 64 inch - 68 inch = 29

No. of men having height more than 68 inch = 27

Now, total shirts are 1500.

So, no. of small shirts to be produced $=\dfrac{44}{100}\times 1500=660$

And no. of medium shirts to be produced $=\dfrac{29}{100}\times 1500=435$

And no. of large shirts to be produced $=\dfrac{27}{100}\times 1500=405$