Question 1: For a draw from a binomial with n = 29 and p = 0.35, what is the theoretical expected value (round to two decimal places)? U = 10.15 Question 2: For a draw from a binomial with n = 29 and p = 0.35, what is the theoretical standard deviation (round to three decimal places)? 0 = 2.56 Question 3: What is your observed sample mean? x = 10.5 Question 4: What is your observed sample standard deviation? S = 2.56 Obtain the histogram of Column 1. Using the histogram you observed and the following rule of thumb to answer the question below: As long as both np 2 5 and n(1 - p) 2 5, the normal is a good approximation to the binomial distribution.Part III. Normal Approximation to the Binomial Make a New Data Table. We'll put 1000 draws from a binomial with n = 29 and p = 0.35. For example, this could be guessing randomly on a multiple choice test with four choices for each question. Recall that to get random draws from the binomial distribution, rst tell J MP how many draws you want by double- clicking on the Column 1 header and putting 1000 in the box to the right of Number of rows, and hitting 0K. Next right-click on the Column 1 header and choose Formula ..., giving you the formula box. JMP Starter L" H v" i O O 0 untitled Column Info... Standardize Attributes... Column Properties New Formula Column D , Insert Columns Delete Columns ['3 Columns (1.11) I; AGalurnn1 mNalUlth-l Label/U nlabel Link ID Sort D. Paste Column Properties Paste Multi Columns Properties ' From the Functions menu, scroll down and choose Random and Random Binomial. Fill in n = 29 and p = 0.35 and hit OK. Here is what JMP looks like with n=10 and p = 0.25: O O I Column1 Filter X E'WW'\" [1" "f ' 3 i J" {13. '4 E \" 9i 5' 5'1 .X, '3 5' AOolumn1 D How D Numeric D Transcendental b Trlgonometric > Character D Comparison D Conditional P Probability D Discrete Probability D Statistical D Random D Date Time P new State D Assignment D Parametric Model D Finance RaudomBinomiul (so , 025] Constants 0 1 2 -1 pi Help Apply Cancel OK , Obtain the histogram of Column 1. Using the histogram you observed and the following rule of thumb to answer the question below: As long as both np 2 5 and n(1 p) 2 5, the normal is a good approximation to the binomial distribution. Question 5: Does the histogram of your sample look approximately normal? How good is the central limit theorem approximation? 0 The distribution looks normal. The central limit theorem works very well here. Q The distribution is not normal whatsoever. The central limit theorem works horribly here. 0 The distribution doesn't look that normal. The central limit theorem doesn't work that well here