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.

The probability that between 6 to 10 pairs of New Balance shoes will be sold next week is .

Step-by-step 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 6)

                          = = .

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204