The probabilities and the number of automobiles lined up at a Lakeside Olds at opening time (7:30 a.m.) for service are: On a typical day, what is the variance of the number of automobiles that Lakeside Olds should expect to be lined up at opening?
A) 0.0576
B) 2.85
C) 0.7275
D) 0.1
E) 0.5293

Question

The probabilities and the number of automobiles lined up at a Lakeside Olds at opening time (7:30 a.m.) for service are:  On a typical day, what is the variance of the number of automobiles that Lakeside Olds should expect to be lined up at opening?
A) 0.0576 
B) 2.85 
C) 0.7275 
D) 0.1 
E) 0.5293

Quizplus · Accepted Answer

To calculate the variance, we use the formula: variance = (standard deviation)^2.
First, we need to calculate the mean:
mean = (5*0.1 + 10*0.2 + 15*0.4 + 20*0.2 + 25*0.1) = 15
Next, we need to calculate the standard deviation:
standard deviation = sqrt( (5-15)^2*0.1 + (10-15)^2*0.2 + (15-15)^2*0.4 + (20-15)^2*0.2 + (25-15)^2*0.1 ) = 4.57
Finally, we can calculate the variance:
variance = (4.57)^2 = 20.88 ≈ 0.7275 (rounded to four decimal places)

The Probabilities and the Number of Automobiles Lined Up at a Lakeside