Question

Sound City sells the ClearTone-400 satellite car radio. For this radio, historical sales records over the last 100 weeks show 3 weeks with no radios sold, 25 weeks with one radio sold, 30 weeks with two radios sold, 30 weeks with three radios sold, 7 weeks with four radios sold, and 5 weeks with five radios sold. Calculate μ_x, σ_x², and σ_x, 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.)

µx _______________.
σ2xσx2 _________.
σx __________.

Answer 1

Let X be the number of ClearTone-400 radios sold at Sound City during a week.

From the given information the probability distribution of X is given by

X=x P(X=x)

0 3/100=0.03

1 25/100=0.25

2 30/100=0.30

3 30/100=0.30

4 7/100=0.07

5 5/100=0.05

Therefore the mean of X is given by:

The variance of X is given by:

The standard deviation of X is: