A sample of voters has been asked to rank two political leaders as to their appeal on a continuous scale of 0 to 10 (0=very unappealing, 10=very appealing). The probability density function of the results is shown below. Select the best interpretation of these results.

In the picture below there are two distributions for separate countries. The distributions represent the height of girls at age 18 measured in metres. Select the answer which best interprets these results. 

Calculate the values of X, where X ~ Students t(d.o.f.=n-1), for which 2.5% of the data lies in the lower tail and 2.5% lies in the upper tail, and where n=50 such that X ~ Students t(d.o.f.=49). (Report the absolute value of your answer to 2 decimal places)

Which of the following statements about the relationship between the standard normal distribution and the Students t distribution are true? (Multiple answers allowed)

(HINT: Look at your answers to Q5-11 to help you answer this question. You can also use the graph you created in the "Distributions" worksheet and see what happens when you change the degrees of freedom in the "=T.DIST()" function.)

Calculate the values of X, where X ~ Students t(d.o.f.=n-1), for which 2.5% of the data lies in the lower tail and 2.5% lies in the upper tail, and where n=100 such that X ~ Students t(d.o.f.=99). (Report the absolute value of your answer to 2 decimal places)

Calculate the values of X, where X ~ Students t(d.o.f.=n-1), for which 2.5% of the data lies in the lower tail and 2.5% lies in the upper tail, and where n=1000 such that X ~ Students t(d.o.f.=999). (Report the absolute value of your answer to 2 decimal places)

Calculate the values of X, where X ~ Students t(d.o.f.=n-1), for which 2.5% of the data lies in the lower tail and 2.5% lies in the upper tail, and where n=20 such that X ~ Students t(d.o.f.=19). (Report the absolute value of your answer to 2 decimal places)

Calculate the values of X, where X ~ Students t(d.o.f.=n-1), for which 2.5% of the data lies in the lower tail and 2.5% lies in the upper tail, and where n=10 such that X ~ Students t(d.o.f.=9). (Report the absolute value of your answer to 2 decimal places)

Instructions:

Use either the "=T.INV.2T()" or "=T.INV()" functions. As a bonus, see if you can work out how to use both functions to give you the same answer!

Calculate the values of Z, where Z ~ N(mean = 0, variance = 1), for which 2.5% of the data lies in the lower tail and 2.5% lies in the upper tail. Use the "=NORM.INV()" function. (Report the absolute value of your answer to 2 decimal places)

Open the worksheet labelled "Distributions" in the “Class Exercise 2 Data.xlsx” file.

In cell B3, calculate the probability associated with the Standard Normal distribution Z value that's in cell A3, using the "=NORM.S.DIST(A3,false)" function. Drag this formula down to calculate the probabilities for the rest of the Z values.

In cell E3, generate the probability associated with the X value from a Student's t distribution with n = 5 (thus the degrees of freedom will equal 4), using the "=T.DIST(D3,4,false)" function. Drag this formula down to calculate the remaining probabilities.

From the graph provided of the resulting distributions, which of the following do you notice?