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

See below

Explanation:

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

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

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

`\bf \sigma^2(x)=(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)=(128.99)/(100)=1.2899`

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

`\bf \sigma(x)=√(variance)`

`\bf \sigma(x)=√(1.2899)=1.1357\;radios/week`