Lakeside Olds can expect around 3 automobiles to be lined up at opening time on average.
To find the expected number of automobiles lined up at Lakeside Olds at opening time, you can use the formula for expected value, which is the sum of the product of each value and its corresponding probability.
The expected value (E) is given by:
E=∑ iP(i)⋅X(i)
where
E is the expected value,
P(i) is the probability of the
i-th value,
X(i) is the
i-th value.
In this case:
E=(0.05⋅1)+(0.30⋅2)+(0.40⋅3)+(0.25⋅4)
E=0.05+0.60+1.20+1.00
E=2.85
So, Lakeside Olds should expect, on average, approximately 2.85 automobiles to be lined up at opening time on a typical day. Since you can't have a fraction of an automobile, you may round to the nearest whole number. Therefore, Lakeside Olds can expect around 3 automobiles to be lined up at opening time on average.
Question
The probability distribution for the number of automobiles lined up at a Lakeside Olds at opening time (7:30 a.m.) for service is:
Number Probability
1 0.05
2 0.30
3 0.40
4 0.25
On a typical day, how many automobiles should Lakeside Olds expect to be lined up at opening time?