Question

Suppose that a local second hand store is selling grab bags for $20 each in order to get rid of excess stock. They have created a total of 300 grab bags, most of which contain various items worth $15 in total. However, there are 40 grab bags which contain items worth $40 in total, 20 grab bags worth $60 in total, and a single grab bath worth $120 in total. Suppose you purchase one grab bag. Let X be the monetary value of a grab bag.

a.Create a discrete probability distribution for X.

b.Find and interpret the mean for X.

c.Find the standard deviation for X

d.Is it worthwhile to purchase a grab bag? Justify your answer.

Answer 1

solution: Total grab bags - 300 - Bags with $40 worth value = 40 with $60 worth value = 20 with $120 worth value = 1 Hence Bags with $15 worth value=300-40 -20-1 = 239 5 (a): Discrete Probability distribution of x , 15 40 60 120 b(x) 239/300 = 0.797 40/300 = 0.133 20/300 = 0.067 1/300 =0.003 . (bi mean of x(x)= 0.797815 + 0.133540 + 0.067x60 +0.0038120 X = 21.68 Interpretation: The mean of x 's 21,88 that - mean by purcharting a grab bag the average monetary value you will get is $21.68.

(c): Standard deviation can be calculated as Elx- (15-21.68 (0.797) + (48-21-68]? (5.33)+ --not (120-21685/6.003) 300 210.4 - 0.837 300 2 (d): OWO As the monetory value of a grab bag is $21.68 with which is greater than $20, the cost of a bag and also the standard deviation is very small. It is worth while to purchase a grab bag.