A die is rolled 60 times.Find the normal approximation to the chance that the face with six spots appears between 9, 10, or 11 times.The exact chance that the face with six spots appears 9, 10, or 11 times?my solution; in one roll of the die P ( 6 spots ) = 1 6 In 60 rolls of the die the expected number of times the face with 6 spots appears is given by E ( X ) = Mean = 60 6 = 10 times. S E ( 6 s p o t s ) = S D = S Q R ( 60 6 ⋅ 5 6 ) = 2.8868Applying the normal approximation to the chance that the face with six spots appears 10 times, I obtain the following: mean = 10 Standard deviation = 2.8868Using the continuity correction of 0.5 the following z-scores are found: z 1 = ( 9.5 − 10 ) / 2.8868 = − 0.1732 and z 2 = ( 10.5 − 10 ) / 2.8868 = 0.1732 Subtracting the cumulative probabilities for the two z-scores gives 0.5688 − 0.4312 = 0.1376 which is the approximate chance that the face with six spots appears 10 times. find the six spots appears between 9,10, or 11?The exact chance that the face with six spots appears 10 times is found from 60 C 10 ( 1 6 ) 10 × ( 5 6 ) 50 = 0.137 find six spots appears 9, 10 or 11 times?

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A die is rolled 60 times.Find the normal approximation to the chance that the face with six spots appears between 9, 10, or 11 times.The exact chance that the face with six spots appears 9, 10, or 11 times?my solution; in one roll of the die   P  (  6   spots  )  =      1    6   In 60 rolls of the die the expected number of times the face with 6 spots appears is given by   E  (  X  )  =  Mean  =      60    6    =  10 times.  S  E  (  6  s  p  o  t  s  )  =  S  D  =  S  Q  R  (      60    6    ⋅      5    6    )  =  2.8868Applying the normal approximation to the chance that the face with six spots appears 10 times, I obtain the following: mean = 10  Standard deviation  =  2.8868Using the continuity correction of 0.5 the following z-scores are found:       z    1    =  (  9.5  −  10  )      /    2.8868  =  −  0.1732 and       z    2    =  (  10.5  −  10  )      /    2.8868  =  0.1732 Subtracting the cumulative probabilities for the two z-scores gives   0.5688  −  0.4312  =  0.1376 which is the approximate chance that the face with six spots appears 10 times. find the six spots appears between 9,10, or 11?The exact chance that the face with six spots appears 10 times is found from  60  C  10            (              1        6            )              10      ×                  (              5        6            )              50        =  0.137 find six spots appears 9, 10 or 11 times?

Gemma Conley · Accepted Answer

Your calculations (as far as I&#039;m able to follow them in your somewhat idiosyncratic exposition) all appear correct. However, they calculate (approximately and exactly, respectively) the probability that a 6 is rolled 10 times. You can apply the same approach to the probabilities that a 6 is rolled 9 times or 11 times, and then add the three results. (In the case of the Gaussian approximation, you can also calculate the sum in one go by subtracting the values of the cumulative distribution function at 11.5 and 8.5.)

polynnxu · Accepted Answer

find six spots appears 9, 10 or 11 times? ANS 60C9×(1/6)^9×(5/6)^51+60C10×(1/6)^10x(5/6)^50+60C11x(1/6)^11x(5/6)^49

A die is rolled 60 times. Find the normal approximation to the chance that the face with six spots appears between 9, 10, or 11 times. The exact chance that the face with six spots appears 9, 10, or 11 times?

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