Question

Let the random variable x be the number of Kellogg's cereals with a certain amount of protein. Construct the discrete probability distribution of x. (Note: Display probability distribution as a table.) Calculate the mean and standard deviation for the probability distribution of x. Interpret the values of the mean and standard deviation in context of the Kellogg’s cereal data. Show your work or calculator syntax.

Kellogs cereal data listed in table

Cereal	Calories (g)	Total Fat (g)	Cholersterol (mg)	Sodium (mg)	Potassium (mg)	Total Carbohydrate (g)
All-Bran	80	1	0	80	350	23
All-Bran Buds	80	1	0	210	300	24
All-Bran Complete	90	0.5	0	210	150	24
Apple Jacks	110	1	0	150	45	25
Apple Jacks with Marshmallows	110	1	0	125	35	26
Cinnabon	120	2	0	115	45	25
Cinnamon Frosted Flakes	110	0	0	150	30	26
Cocoa Krispies	120	1	0	120	55	27
Corn Flakes	100	0	0	200	45	24
Corn Pops	120	0	0	105	30	27
Cracklin Oat Bran	200	7	0	135	200	34
Crispix	110	0	0	190	20	25
Despicable Me 3	120	1	0	150	55	27
Disney Princess	120	1	0	150	55	27
Froot Loops	110	1	0	150	45	25
Froot Loops Bloopers	110	1	0	150	40	25
Froot Loops with Marshmallows	110	1	0	115	35	26
Frosted Flakes	110	0	0	150	35	26
Frosted Flakes Choco Zucaritas	120	1	0	160	55	26
Frosted Flakes Chocolate with Marshmallows	120	1	0	140	50	26
Frosted Flakes with Marshmallows	110	0	0	135	30	26
Frosted Krispies	150	0	0	130	20	27
Frosted Mini-Wheats	190	1	0	0	200	46
Frosted Mini-Wheats Blueberry	190	1	0	0	190	47
Frosted Mini-Wheats Little Bites	200	1	0	0	210	27
Frosted Mini-Wheats Little Bites Chocolate	200	2	0	210	270	46
Frosted Mini-Wheats Maple Brown Sugar	190	1	0	0	190	47
Frosted Mini-Wheats Strawberry	190	1	0	0	190	47
Frosted Mini-Wheats Touch of Fruit in the Middle Raspberry	190	1	0	10	190	45
Honey Smacks	110	0.5	0	40	50	25
Keebler	130	3.5	0	140	50	24
Krave Chocolate	130	3.5	0	95	75	24
Krave Double Chocolate	120	3.5	0	95	95	23
Mini-Wheats Unfrosted	190	1	0	0	250	45
Mueslix	200	3	0	130	180	41
Raisin Bran	190	1	0	210	390	46
Raisin Bran Crunch	190	1	0	200	210	45
Raisin Bran Crunch Apple Strawberry	180	1	0	190	190	42
Raisin Bran with Cranberries	200	1	0	210	210	50
Raisin Bran with Flaxseeds	180	1.5	0	190	140	44
Rice Krispies	130	0	0	160	30	29
Rice Krispies Treats	120	1	0	170	15	26
Smart Start	190	1	0	200	90	43
Smorz	120	2	0	135	40	25
Special K	120	0.5	0	210	15	23
Special K Apple Cinnamon Crunch	120	1.5	0	200	70	27
Special K Blueberry with Lemon Clusters	120	1	0	160	75	27
Special K Chocolate Almond	110	1.5	0	150	85	23
Special K Chocolately Delight	120	2	0	180	80	25
Special K Fruit and Yogurt	120	1	0	140	70	27
Special K Multigrain Oats and Honey	100	0.5	0	140	70	25
Special K Nourish Apple Raspberry Almond	190	2.5	0	170	170	41
Special K Nourish Coconut Cranberry Almond	200	4	0	160	150	40
Special K Protein	120	1	0	190	125	19
Special K Protein Cinnamon Brown Sugar Crunch	110	1	0	190	60	22
Special K Pumpkin Spice Crunch	120	1.5	0	200	70	27
Special K Red Berries	110	0	0	190	70	27
Special K Vanilla Almond	110	1.5	0	170	80	25

Answer 1

	Calories (g)						cumulative
lower		upper	midpoint	width	frequency	percent	frequency	percent
80	<	99.99	90	20	3	5.2	3	5.2
100	<	119.99	110	20	16	27.6	19	32.8
120	<	139.99	130	20	20	34.5	39	67.2
140	<	159.99	150	20	1	1.7	40	69.0
160	<	179.99	170	20	0	0.0	40	69.0
180	<	199.99	190	20	12	20.7	52	89.7
200	<	219.99	210	20	6	10.3	58	100.0
					58	100.0

mean	138.45
sample standard deviation	38.01