The 95% condence interval for the mean monthly earnings for January is [$9,000; $15,000]. Are the following remarks true or false?

(a) If I were to run a new simulation for monthly earnings in January, there is a 95% chance that the observed sample mean of my simulation would be between $9,000 and $10,000.

(b) If I were to run one simulation of 200 trials, then in only 10 trials, the value obtained for the monthly earnings would not be between $9,000 and $10,000'.

In the stimulation, 900 trials were used.

(c) 'I noticed that your condence interval has a range of $1,000. So, if I were to run a simulation with 900 trials as well, I would also obtain a 95% condence interval with a range of $1,000'.

(d) 'Given the results of your simulation, a 99% condence interval for the mean monthly earnings of January would have a range larger than $1000'.