Probability over $50$-day ranges to predict results on one day The title is a bit complex, so I'll just post the question. This is in preparation for a final I'm going to take.

Consider the total number of cars that a car dealership might sell over $50$ randomly selected (contiguous) days. Assume that the expected value of the number of cars sold over such a random sample of $50$ days is $62$ cars and that the standard deviation is $7$ cars.
The question I'm having trouble with is: What can you say about the probability that the dealership sells more than $1$ car on a randomly selected day?

I answered that you can't say anything, because all you know is the probability for a sample of $50$ days, which means all the cars could theoretically be sold on one day, or they could be sold evenly over the course of $50$ days. Apparently, this answer is incomplete.
I can't figure out what you could possibly gather from the information given; any help would be greatly appreciated. Thanks.
 A: Let $X$ be the demand over the 50-day period. Let $Y$ be the daily demand. Using the model $Y = {X \over 50}, $ we have $E[Y] = {62 \over 50} = 1.24$ and $\sigma_Y^2 = {\sigma_X^2 \over 2500}=0.0196,$ or $\sigma_Y = 0.14$ 
Now you are interested in $P[Y \geq 1]$. Instead, think about $P[Y \leq 1]$ and use Chebyshev's inequality. At $Y = 1,$ the number of standard deviations you are distant from the mean of 1.24 is ${0.24 \over 0.14} =1.7143 $ and using the one-sided version of Chebyshev's inequality:
$P[Y \leq \mu - k \sigma ] \leq {1 \over k^2 +1} ,$ we find $P[Y \leq 1] \leq 0.2539$
Now convert that to the complementary 
$P[Y \geq 1] > 0.7461$ 
Another model is to let the daily demand, call it $D_i,$ be such that the demand over the 50 days is $X = \sum D_i .$ If we assume the daily demands are independent, then we require $E[D_i] = {62 \over 50}$ and $\sigma^2_{D_i} = {49 \over 50} $ so the variance over the 50 day period will be $49.$ 
Following the same Chebyshev logic as in the first model, I find 
$P[D_i \geq 1] > 0.0555$
Given the large difference and the even more extreme example whuber noted, can the OP get us more information?
