Question

The following data show the number of pairs of men's New Balance sneakers that were sold over the last 25 weeks at a discount shoe store.

1 4 6 6 8
8 9 11 11 11
12 12 14 14 14
15 17 17 17 19
19 20 21 24 24
Construct a relative frequency distribution for this data and determine the probability that between 6 to 10 pairs of New Balance shoes will be sold next week.

Answer 1

The probability that between 6 to 10 pairs of New Balance shoes will be sold next week is
`(3)/(25)` .

Explanation:

We are given the following data that show the number of pairs of men's New Balance sneakers that were sold over the last 25 weeks at a discount shoe store below;

1, 4, 6, 6, 8, 8, 9, 11, 11, 11 , 12, 12, 14, 14, 14, 15, 17, 17, 17, 19, 19, 20, 21, 24, 24.

Now, preparing the relative frequency distribution for this data;

No. of pairs of men's Frequency (f) Relative frequency

New Balance sneakers (X)

1 1 1

4 1 2

6 2 4

8 2 6

9 1 7

11 3 10

12 2 12

14 3 15

15 1 16

17 3 19

19 2 21

20 1 22

21 1 23

24 2 25

Total 25

Here the frequency of 2 against 6 represents that 6 is occurring 2 times in our given data.

Now, the probability that between 6 to 10 pairs of New Balance shoes will be sold next week is given by = P(6 < X < 10)

P(6 < X < 10) = P(X < 10) - P(X
`\leq` 6)

=
`(7)/(25) - (4)/(25)` =
`(3)/(25)` .