How to identify if Population Standard Deviation is Known/Unknown?

Hello! I'm having a difficult time identifying from word problems the difference between sample standard deviation and population standard deviation.

I am covering the chapter on hypothesis testing and it states that it depends on whether population standard deviation(sigma) is known or unknown. If sigma is known, I used the z-distribution table, if sigma is unknown I must use the t-distribution table.

My question is, can someone explain to me, using the following two problems, how to spot which key terms to determine whether the population standard deviation is known or unknown. They both use the term "standard deviation" and therefore confuse me. All help is appreciated, thank you very much!

Population Standard Deviation Known: Use Z Distribution

Before the hiring of an efficiency expert, the mean productivity of a firm’s employees was 45.4 units per hour, with a standard deviation of 4.5 units per hour. After incorporating the changes recommended by the expert, it was found that a sample of 30 workers produced a mean of 47.5 units per hour. Using the 0.01 level of significance, can we conclude that the mean productivity has increased?

Population Standard Deviation Unknown: Use T Distribution

A scrap metal dealer claims that the mean of his cash sales is “no more than $80,” but an Internal Revenue Service agent believes the dealer is untruthful. Observing a sample of 20 cash customers, the agent finds the mean purchase to be $91, with a standard deviation of $21. Assuming the population is approximately normally distributed, and using the 0.05 level of significance, is the agent’s suspicion confirmed?