Question

Sound City sells the ClearTone-400 satellite car radio. For this radio, historical sales records over the last 100 weeks show 5 weeks with no radios sold, 27 weeks with one radio sold, 27 weeks with two radios sold, 27 weeks with three radios sold, 9 weeks with four radios sold, and 5 weeks with five radios sold. Calculate μx, σx2, and σx, of x, the number of ClearTone-400 radios sold at Sound City during a week using the estimated probability distribution. (Round your answers to 2 decimal places.)

Answer 1

Answer:

μ =2.23

$\sigma_x^2= 1.49$

$\sigma_x=1.22$

Step-by-step explanation:

Radio(x)                            weeks                           P(x)

0                                         5                                 5/100 = 0.05

1                                           27                               27/100=0.27

2                                          27                                 27/100 = 0.27

3                                         27                                 27/100 = 0.27  

4                                           9                                    9/100=0.09

5                                             5                                    5/100=0.05

We know that

Mean ,μ

$\mu =\sum x.P(x)$

μ = 0 x 0.05 + 1 x 0.27 + 2 x 0.27 + 3 x 0.27 + 4 x 0 .09 + 5 x 0.05

μ =2.23

$\sigma_x^2= \sum x^2\times P(x)-(\sum x.P(x))^2$

$\sigma_x^2= 0^2\times 0.05+ 1^2\times 0.27+ 2^2\times 0.27+ 3^2\times 0.27+ 4^2\times 0.09+5^2\times 0.05-2.23^2$

$\sigma_x^2= 1.49$

$\sigma_x= \sqrt{\sigma_x^2}$

$\sigma_x=1.22$