Question

The number of M&Ms in a fun size pack has on average 10 candies with a varianc n average 10 candies with a variance of 4 candies. If you are given a single fun size pack of M&Ms: a. What can we say about the probability that your pack of M&Ms does not have between 9 and 11 candies? b. How useful do you find this information to be? For a class activity in STAT 3600, each of the 35 students gets a pack of M&Ms to work with. c. What is the distribution (including parameter values) of the total number of M&Ms that will be used in class? d. What is the probability that the average number of M&Ms in a pack of M&Ms used in class is between 9.5 and 10.5 candies? e. Would the variance in the average number of candies in a pack increase or decrease if the same exercise was repeated in a class with 80 students?

Answer 1

Answer Given Data, Mean Average fun pack size = 10 candies : 4 candies Variance @ The probability of M&Ms pack does not have between 9 and I candies - 1-PC90x211] To compute Pr (9sxsu) Corresponding the z-values needed to be computed are : - 9-10 z, : sno:-0.5 X2-4 o - 0.5 Zz = 11-16 .. we get Pr (95*311) = pr 19 20 czs 2) pr (95x411) = P1(-0.5 € 240.5) pr (9<x<11) = pr ( 280.s)- P(Z 8-0.5)

.6915-0.3085 - 0.3829 X 211) 1-0.3829 = 0.6171. 6 Useful do you find this information to be :- = = Since i most of the data (61.71%) does not lies between 9 and il we can interpret a lot of things out of this. © The total number of M&M's that will be used in class is Mean will remain same = mean = 10 Variance will be reduced to a < =0.114 35 Variance = 0.114 @ Probability of Meri's in a pack used in a class between 9.5 and 10.5 candies: Je will use S: Savt (0.116) → to compute pr(95$*$10.5). » The corresponding 2 - values needed to be computedare:

X -4 4.5 - 10 zii- 0.338 : -1.48 za X2-04 2 10.5-10 0.33€ = 1.48 .. we get : pr (9.5<*$10.5) = P1 19.5-10 10.5 -10 10.338 0.338 pr (9.5 5x510.5) - Pr(-1-48 2 €1.) pr (9.5 ¢x¢10:5) pr (23148) - pr ( 29-1.) pv (9.5 5x<10.5) - 0.9305 - 0.0695 pr (9.5 < x < 10.5): 0.8609 @ The variance in the average of candies in a pack increase 181, decrea se Repeated in a class with = 80 students. The sample size increases the variance decreases. variance will reduce to 4/80 = 0.05 from 0.1