Determine the marginal probability distribution of x1 blank

Question

Question 1

1. The height of a typical American male adult is normally distributed with a mean of 68 inches and a standard deviation of 5 inches. We observe the heights of 12 American male adults.

   a) What is the probability that exactly half the male adults will be less than 62 inches tall? Blank 1

   b) Let Y be the number of the 12 male adults who are less than 62 inches tall. Determine the mean Blank 2 and standard deviation of Y Blank 3.

Question 2

1. A sporting goods store sells two competing brands of softball bats. Let x1 and x2 be the numbers of the two brands sold on a typical day at the store. Based on the store historical data, the conditional probability distribution of x1 given x2 is assessed and provided in the table below. The marginal distribution of is also given in the bottom row of the table.

   Sales of Brand 1, Given sales of Brand 2
   
   

   	x2= 0	x2= 1	x2= 2	x2= 3
   x1= 0	0.05	0.15	0.25	0.30
   x1= 1	0.10	0.25	0.55	0.57
   x1= 2	0.60	0.50	0.15	0.10
   x1= 3	0.25	0.10	0.05	0.03
   Marginal Distribution of x2	0.20	0.30	0.30	0.20

   
   Are x1 and _x2independent random variables Blank 1
   Determine the marginal probability distribution of x1 Blank 2Given that no brand x2 bats are sold on a given day, what is the probability of observing the sale of at least one brand x1 bats at this sporting goods store?