Use the Student's t-distribution to find the t-value for each of the given scenario. Round t-values to four decimal places.

- Find the value of t such that the area in the left tail of the t-distribution is 0.005, if the sample size is 122.

t =---

Find the value of t such that the area in the right tail of the t-distribution is 0.1, if the sample size 35.

t = ----

Find the value of t such that the area in the tail of the t-distribution is 0.0005, if the sample size is 101.

t = ---

Find the two values of t such that 99.9% of the area under the t-distribution is centered around the mean, if the sample size is 141. Enter the solutions using a comma-separated list.

t =-

2- The following confidence interval gives a range of likely values for the average commute distance of all students attending class at the main campus of IRSC. (13, 15.6)

Determine the point estimate (x) and margin of error (E) used to construct this particular confidence interval.

x = ---

E =--

3- An economist would like to estimate the average household income in Okechobee county. The mean household income of a random sample of 254 families in Okechobee county was found to be $37,893. The standard deviation of the household incomes of all households in Okechobee county is known to be $956.

Using a 98% confidence leve, determine the margin of error, E, and a confidence interval for the average household income in Oechobee county. Report the confidence interval using interval notation. Round solutions to two decimal places, if necessary.

The margin of error is given by E =

A 98% confidence interval is given by =---

4- An agonomist would like to estimate the average weight of all Indian River County grapefruits. The mean weight of a random sample of 171 Indian River County grapefruits was found to be 232 grams. The standard deviation of the weights of all Indian River county grapefruit is known to be 25 grams.

Find three different confidence intervals - one with 99% confidence level, one with 95% confidence level, and one with 90% confidence level - for the mean weight of all Indian River county grapefruits. Notice how the confidence level affects the margin of error and the width of the interval.

Report confidence interval solutions using interval notation. Round solutions to two decimal places, if necessary.

- The margin of error for a 99% confidence interval is given by E =

A 99% confidence interval is given by = --

- The margin of error for 95% confidence interval is given by E =

A 95 % confidence interval is given by = --

- The margin of error for 90% confidence interval I given by E =

A 90% confidence interval is given by =