This would be the same as if population standard deviation was unknown and we were to use sample standard deviation, while n>30. Also in case n<30 and population standard deviation is known this formula is still valid given the underlying distribution of each sample observation is normal. c) Using item a) and the central limit theorem of sample proportion which is ~ N(0, 1) Vm/n Show that P(p – Za/2\ < p< p- %a/2 = 1- a Note that above is the confidence interval for population proportion; however, since it envolves the unkown population proportion p, sample proportion will be used instead. d) Where the students t distribution was discovered ? why it was called this way ? in what situation confidence intervals of population mean need to be made based on this distribution ? What was the application of it when it was discovered ? Which one is true: when its degree of freedom increases it diverges or converges to the normal distribution ?

Choose the correct calculation to be made for the scenario below. For your birthday party you bought some balloons and need to make sure you buy enough helium to fill them all. Surface Area Volume Area O Perimeter O Lateral Surface Area

Rectangle $ABCD$ABCD​ is translated and then reflected to create rectangle $A'B'C'D'$A′B′C′D′​ . Do rectangle $ABCD$ABCD​ and rectangle $A'B'C'D'$A′B′C′D′​ have the same area? Justify your answer. Respond in the space provided.

CLOSET BEDROOM 2 9.5 x 12.5 OPPO A16 Shot by DickyG.♥ LIVING ROOM 11 x 17.5 Mavis decided to tile the living room using a marble tile. The dimensions of the tiles are given below. TABLE 2: DIMENSIONS OF TILES Tile type Rectangular Square Length Width 900 mm 600 mm 0,5 m 0,5 m [www.chntile.com] Use TABLE 2 to answer the questions that follow. 4.3.1 Mavis claims that she will need a minimum of 30 rectangular tiles to tile the living room only. 4.3.2 Verify, showing ALL calculations whether her statement is valid. It takes tilers 45 minutes to lay 15 tiles and 25 minutes to grout the whole living room. Mavis claims that the tilers will finish tiling the living room at 9:28 if they started at 8:15 in the morning. Verify, showing ALL calculations, whether her statement is valid. (6) [30]