Find α for this dice rolling game.There is the point A(10) on the number line. Let's following the die rolling game rules like below with its pips are 1 to 6 as commonly we've known.- The 1st rule) A point moves as much as +2[positive direction with magnitude 2] for the even pips like 2,4 and 6- The 2nd rule) A point moves as much as −1[negative direction with magnitude 1] for the odd pips like 1,3 and 5.After doing this trial 100 times, "A" lied on the right direction compared with 90. We get P ( Z ≥ α ) considering the continuity correction. Find the real number α. (Z is the random variable following normal distribution.)From here, my solution starts. Let the X i be the movement of a point for ith trial (Here Each i, 1 ≤ i ≤ 100) X i 2 − 1 p ( X i ) 1 / 2 1 / 2 1 From the table I got E ( X i ) = 1 2 and V ( X i ) = 9 4 So only have to consider is X ( = X 1 + X 2 + . . . + X 100 ) &gt; 80, Plus E ( X ) = 50 and V ( X ) = 15 2 Therefore P ( X ≥ 80.5 ) = P ( Z ≥ 80.5 − 50 15 ) from continuity correction for P ( X &gt; 80 ). (In other words, α = 61 30 ( = 30.5 15 ) )The answer sheet claimed the α = 2.1. I can't find any errors in my solution. Please let me know which points did I wrong.p.s.) The answer sheet solution. (The reason why the author claimed 2.1).Say Y be the number of the even pips doing the 100 times trials, Then only just find P ( 10 + 2 Y − ( 100 − Y ) &gt; 90 )In other words P ( Y ≥ 61 ). Since the Y~B(100,1/2), P ( Y ≥ 61 ) = P ( Y ≥ 60.5 ) = P ( z ≥ 2.1 )

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Find   α for this dice rolling game.There is the point A(10) on the number line. Let&#039;s following the die rolling game rules like below with its pips are 1 to 6 as commonly we&#039;ve known.- The 1st rule) A point moves as much as +2[positive direction with magnitude 2] for the even pips like 2,4 and 6- The 2nd rule) A point moves as much as −1[negative direction with magnitude 1] for the odd pips like 1,3 and 5.After doing this trial 100 times, &quot;A&quot; lied on the right direction compared with 90. We get   P  (  Z  ≥  α  ) considering the continuity correction. Find the real number   α. (Z is the random variable following normal distribution.)From here, my solution starts. Let the       X    i   be the movement of a point for ith trial (Here Each i,   1  ≤  i  ≤  100)                              X          i                            2                    −        1                                  p        (                  X          i                )                    1                  /                2                    1                  /                2                    1            From the table I got   E  (      X    i    )  =      1    2   and   V  (      X    i    )  =      9    4  So only have to consider is   X  (  =      X    1    +      X    2    +  .  .  .  +      X          100        )  &amp;gt;  80, Plus   E  (  X  )  =  50 and   V  (  X  )  =      15    2  Therefore   P  (  X  ≥  80.5  )  =  P  (  Z  ≥            80.5      −      50        15    ) from continuity correction for   P  (  X  &amp;gt;  80  ). (In other words,   α  =      61    30    (  =      30.5    15    ) )The answer sheet claimed the   α  =  2.1. I can&#039;t find any errors in my solution. Please let me know which points did I wrong.p.s.) The answer sheet solution. (The reason why the author claimed 2.1).Say Y be the number of the even pips doing the 100 times trials, Then only just find   P  (  10  +  2  Y  −  (  100  −  Y  )  &amp;gt;  90  )In other words   P  (  Y  ≥  61  ). Since the Y~B(100,1/2),   P  (  Y  ≥  61  )  =  P  (  Y  ≥  60.5  )  =  P  (  z  ≥  2.1  )

Dana Simmons · Accepted Answer

Step 1Note that   P  (  Y  &amp;gt;  60  )  =  P  (  X  &amp;gt;  90  ). The difference only comes into play when you add the continuity correction factor. The standard deviation of X is three times as great as the standard deviation of Y (because the distance between -1 and 2 is three times as great as the distance between 0 and 1). Therefore the continuity correction on X is       1    3   as significant as the continuity correction on Y.Step 2So I would say that both the &quot;official&quot; answer (  α  =  2.1) and your solution (  α  =  2.03333...) are reasonable approaches, with the difference being due to the relative importance of 1 unit of X compared to 1 unit of Y.

Find alpha for this dice rolling game. There is the point A(10) on the number line. Let's following the die rolling game rules like below with its pips are 1 to 6 as commonly we've known.

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