Question

In a quarter-pound bag of red pistachio nuts, some shells are too 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 distribution given in the table below. X 0 p(x) 0.500 3 4 5 0.250 0.100 0.050 0.065 0.035 (a) Is this a valid probability distribution? Justify your answer. (Select all that apply.) This is a valid probability distribution since ✓ p(x) = 1. This is a valid probability distribution since O s p(x) < 1. This is not a valid probability distribution since s p(x) > 1. This is not a valid probability distribution since p(x) < 0. This is not a valid probability distribution since p(x) < 1. (b) Find the mean, variance, and standard deviation of X. (Round your variance and standard deviation to four decimal places.) mean variance standard deviation (c) Find the probability X takes on a value less than the mean. (d) 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?

Answer 1

9 @ This is a valid prob. des tribution Since EP(X) = 0.500+ 0.250+-+0.035=1 meana Erupa)0(0.5)+1(0,250) + 2(0.100)+ - +5(0.035)-(1.035) (x2)= {x2D(04): 0(0.500)+12 (0.250)+ . 2 10.100)+*+540.035)- 3.015 Voux), ECx2)- ECO))? 3.015-(1.035)2 -1.9438] stel.dew Varixi = 11.3942] P(x2 M): P(X<1.035). O. 500+ 0. 250 0.750

P*?4): 0.065 +0.0352 0.100 Prob (Both bags have x>4) = 0.100)- (0.100):10.0100|| 1° No of pistachios considered independent from bag to bag, 80 probability medeciplied)