In a quarter pound bag of red pistacio nuts, some shells are to difficult to pry

Question

In a quarter pound bag of red pistacio nuts, some shells are to difficult to pry open by hand. Suppose the random variable X, the number of pistachios in a randomly selected bag that cannot be opened by hand, has the probability distrubution given in the table below. x 0 1 2 3 4 5 p(x) .5 .25 .1 .05. .075 .025 a.) Find the probability X takes on a value less than the mean b.) Suppose two bags of pistachios are selected at random. What is the probability that both bags have four or more pistachios too dificult to open by hand?

Explanation / Answer

f=   1  
fx =   1.025  
      
Mean = fx / f =   1.025  
Mean square = f x^2 / f =   2.925  
      
Varriance = (Mean square) - (Mean)^2      
      
Varriance = f x^2 - Mean^2 =   1.874  
Stadard Dev= Var =   1.369  

a.
P( X < less than mean) = P( X < 1.025) = P(X=0) + P(X=1) = 0.5 + 0.25 = 0.75

b.
P(pistachios are selected at random and bags have four or more pistachios ) =    0.075 + 0.025 = 0.1

Values ( X ) P(X) px ( X^2) f x^2 0 0.5 0 0 0 1 0.25 0.25 1 0.25 2 0.1 0.2 4 0.4 3 0.05 0.15 9 0.45 4 0.075 0.3 16 1.2 5 0.025 0.125 25 0.625

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