In interval estimation, the t distribution is applicable only when

a. the population has a mean of less than 30.

b. the sample standard deviation is used to estimate the population standard deviation.

c. the variance of the population is known.

d. the mean of the population is unknown.

b. the sample standard deviation is used to estimate the population standard deviation.

Correct since that's the best approximation in order to use the t distribution to estimate the mean

Step-by-step explanation:

For this problem let's analyze the possible options:

a. the population has a mean of less than 30.

False since the mean can be any value and not makes sense

b. the sample standard deviation is used to estimate the population standard deviation.

Correct since that's the best approximation in order to use the t distribution to estimate the mean

c. the variance of the population is known.

False if the variance is know we can use the z distribution for the confidence interval and is not neccessary the t distribution

d. the mean of the population is unknown.

False we create the confidence interval since we don't know the true mean beacuse if we know the mean we don't need to create an interval