Good signs that it is a scam:
1) They found you rather than you initiating the contact by signing up with them
2) They pay an amount that seems generous for the work and time involved
3) They are asking you to receive money in advance of your work
As soon as they say they are paying $150 and it doesn't take more than a full day of work on your part, you should have your answer to the question. The #1-3 above are just additional hints.
The scam works by sending you a legitimate looking check, usually a forgery with the name of an actual mystery shopping company or close enough that if/when you look them up on the internet you are likely to find a same or similarly named legitimate company.
The bank account number on the check is likely to be real, so if the bank calls ahead, there is enough money in the account to cover the check.
The check will be bounced as a forgery either by the paying bank or by the real owner of the account.
Let me suggest for a moment that you send a Christmas check for $5 to your nephew Johnny. Lets say that I am a thief who steals the mail from Johnny's mailbox. I go to my computer and I can print perfectly legitimate checks, but I print your account number from the check you wrote Johnny. I 'issue' checks out using your account number for $276 and sign them "Mickey Mouse" in an appropriate scribbly hand. The chances are good that one or more of these checks will 'clear' against your account balance, but when you complain or your bank bothers to check the signatures, they will bounce the check back through the system and the money will be duly deducted from the account of the person who deposited the check. This process is likely to take several weeks, and assuming that the person who deposited the check waited their 7-10 for the check to be marked 'cleared' by their bank and ran off and spent the money, the bank will be calling them to make up the missing funds. They will also be charging fees for the service of recovering their lost funds.