I am stuck on trying to understand what seems like a simple problem!
"A store manager predicts that his sales for a certain day of the week will be $\$150,000.00$. An independent assessor following the store's day-to-day sales says that the probability of the store's sales for this same day being $\geq \$150,000$ is $0.35$. Therefore, what is a more reasonable estimate for the store's sales for the day?"
The only thing I could think of was to compute $150000 \cdot 0.35 = 52500$, but I don't know why this should be correct. Any ideas?
Thanks!
There is not enough information to answer the problem. If we accept the assessor's statement as truth, it could be that the store sells $149,000$ on $65\%$ of the days and $1,000,000$ on $35\%$ of the days. They could sell nothing on $65%$ of the days and $150,001$ on $35\%$ of the days. We could easily come up with a distribution where the expected sales are truly $150,000$ even though the store falls short $65\%$ of the time.