We use a t distribution for inference about a population mean instead of the standard normal distribution:

a. if we do not know the population mean and must use the sample mean.
b. if the original population does not have a normal distribution.
c. if we do not have a simple random sample.
d. if we do not know the population standard deviation and must use the sample standard deviation.

d. if we do not know the population standard deviation and must use the sample standard deviation.

Step-by-step explanation:

We use t-distribution is quite similar to distribution of z-score .

The interpretation of t-scores and z-scores are same.

T- distribution is used when the  data is not accurately normal and when the population standard deviation is  unknown.

In the absence of population standard deviation , we use the standard deviation of the sample.

So , We use a t distribution for inference about a population mean instead of the standard Normal distribution if we do not know the population standard deviation and must use the sample standard deviation.

Hence, the correct option is : d. if we do not know the population standard deviation and must use the sample standard deviation.