Random variables (RVs) ‘X’ and ‘Y’ represent annual incomes of well established unmarried young professional men and women. These two RVs are normally distributed and are statistically independent. The mean values of ‘X’ and ‘Y’ are $100K and $80K with standard deviations of $20K and $15K respectively. Here ‘K’ represents units of thousands.

a.A random sample of 25 professional men is taken to find their average income. What is the probability that this mean income of the sample is less than $90K. For professional men, the population standard deviation given is considered reliable. If this event does occur, what conclusion can you draw?

b.A random sample of 20 professional women is taken to find their average income. However, the population standard deviation is considered unreliable and is estimated for this sample to be $22K. What is the probability that this mean income of the sample is more than $91.3932K. If this event does occur, what conclusion can you draw?

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In the answers, a) uses the Z-score and b) uses the t-score. I'm confused because I thought the rule of thumb was for samples under 30 that the t-score should be used. Can someone further explain this to me please?