Question

Sound City sells the ClearTone-400 satellite car radio. For this radio, historical sales records over the last 100 weeks show 4 weeks with no radios sold, 33 weeks with one radio sold, 39 weeks with two radios sold, 12 weeks with three radios sold, 8 weeks with four radios sold, and 4 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.

Answer 1

Answer:

See below

Step-by-step explanation:

$\bf \mu(x)$ is the average

$\bf \mu(x)=\frac{4*0+33*1+39*2+12*3+8*4+4*5}{100}=\frac{199}{100}=1.99\;radios/week$

$\bf \sigma^2(x)$ is the variance

$\bf \sigma^2(x)=\frac{4*(0-1.99)^2+33*(1-1.99)^2+39*(2-1.99)^2+12*(3-1.99)^2+8*(4-1.99)^2+4*(5-1.99)^2}{100}=\frac{128.99}{100}=1.2899$

$\bf \sigma(x)$ is the standard deviation

$\bf \sigma(x)=\sqrt{variance}$  

$\bf \sigma(x)=\sqrt{1.2899}=1.1357\;radios/week$