Some notes on finite population correction factor:
If the population is small and the sample is large (more than 5% of the small population), use the finite population correction factor.
For standard error of the mean, use:
sd/√n
If you need to adjust for the finite population correction factor, use:
sd/√n * √(N-n)/N-1)
N = number in population
n = number in sample
Therefore:
a. Use the formula sd/√n (population is infinite)
b. Is the sample size of 40 more than 5% of the population? No, it isn't; your answer will be the same as part a).
c. Is the sample size of 40 more than 5% of the population? No, it isn't; your answer will be the same as part a) and b).
d. Is the sample size of 40 more than 5% of the population? Yes, it is, so use the finite population correction factor.
I hope this will help get you started.