Question $1$

Using the $z$ table, find the critical value $($or values, give positive CV if two$-$tailed$).$

a$.=0\mathrm{.}01,$ right $-$ tailed $n=99$

Question $2$

A survey of $19$ individuals who passed the seven exams and obtained the rank of Fellow in the actuarial field

finds the average salary to be $$166617$ and the standard deviation for the sample is $$14000.$ Solve the

problem below and express your final answer in $3$ decimal places whenever necessary.

a$.$ At $99\%$ level, what is the positive value of the margin of error for all Fellows?

b$.$ Find the $99\%$ lower confidence limit for all Fellows.

c$.$ Using the $t-$distribution table, what is the absolute value of $t($alpha over $2)$ at $99\%$ level?

d$.$ Find the $99\%$ upper confidence limit for all Fellows.

e$.$ What is the negative value of the maximum error of estimate for all Fellows at $99\%$ level?