please show all steps thanksSolutionA Here we use the binomi

please show all steps. thanks!

Solution

A)

Here, we use the binomial probabilitiy distirbution formula.

Note that the probability of x successes out of n trials is

P(n, x) = nCx p^x (1 - p)^(n - x)

where

n = number of trials = 3000000
p = the probability of a success = 1/6 = 0.166666667
x = the number of successes = 5

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If you use factorials for the combination part, the calculator may not be able to handle it, so you should use combinations function. The exponent is also too high for 1 - p here, so if you calculate that separately, you might only get 0.

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b)

We first get the z score for the critical value:          
          
x = critical value =    498999.5      
u = mean = np =    500000      
          
s = standard deviation = sqrt(np(1-p)) =    645.4972244      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    -1.549967935      
          
Thus, the left tailed area is          
          
P(z >   -1.549967935   ) =    0.939425394 [ANSWER]