In a quarter-pound bag of pistachioo nuts, some shells are too difficult to pry

Question

In a quarter-pound bag of pistachioo nuts, some shells are too difficult to pry open by hand. Suppose the random variable x, ththe number of pistachios in a randomly selected bag that cannot be o opened by had, has the probability distribution given in the table below.

a) Find the mean of X.

b) Find the probability x taskes on a value less than the mean.

c) Suppose two bags of pistachios are selected at random. What is the probability that both bags have four or more pistachios too difficult to open by hand?

I have found the a and c, but am confused on finding b. Is b just P(0)?

0 1 2 3 4 5 0.6 0.15 0.1 0.075 0.05 0.025

Explanation / Answer

f=   0.46  
fx =   0.9  
      
Mean = fx / f =   1.9565  
Mean square = f x^2 / f =   5.7609  
      
Varriance = (Mean square) - (Mean)^2      
      
Varriance = f x^2 - Mean^2 =   1.933  
Stadard Dev= Var =   1.39  

a)

Mean = 1.9565

b)

P( X < 1.9665) = P(X=1)+P(X=0) = 0.6+0.15 = 0.75

c)

P( 4 or More) = P(X=4)+P(X=5) = 0.05+0.025 = 0.075

Values ( X ) Frequency(f) fx ( X^2) f x^2 0 0.06 0 0 0 1 0.15 0.15 1 0.15 2 0.1 0.2 4 0.4 3 0.075 0.225 9 0.675 4 0.05 0.2 16 0.8 5 0.025 0.125 25 0.625

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