Question

Harley's Daycare will run a promotional raffle that offers a chance to win either a lifetime discount on merchandises (which results in a $1,000 savings) or a 5-year limited discount on any party-goods (which results in a $100 savings).

• Winning a lifetime discount has a 1-in-500 chance.

• Winning a 5-year limited discount has a 1-in-50 chance.

Is this promotion worth it if the tickets cost $15?

The promotion is not worth it.

ONLY if you cannot answer F1, for partial credit (6 points) answer F2.

[F1 (13 points)] Some additional collected data is presented in the table below:

Enrollment Camp/DayCare	Infants (I)	Toddler (2-3Y) (T)	PreK_K (K)
ParentsOasis (PO)	0	10	50	60
SunAndFun (SF)	8	32	20	60
NoPlaceLikeHome (NH)	10	20	40	70
	18	62	110	190

Give the literal formula first (not with numbers) and then solve: “what is the probability of not being a Toddler?”	P(not toddler) = P(infants) + P(pre k)                           = 9.47   + 57.89                           = .6736----->67.4%
Give the literal formula first (not with numbers) and then solve: “What is the probability of being an infant or toddler given that you are attending the NoPlaceLikeHome camp?”
Give the literal formula first (not with numbers) and then solve: “what is the probability of being a Pre-K_K child attending ParentsOasis camp?”
Give the literal formula first (not with numbers) and then solve: “What is the probability of being in the Toddler or PreK_K group and attending SunAndFun.”
Is there any relationship between being a toddler and attending a specific Camp/Daycare? Explain based on “given” probabilities values.

F2. Partial Credit. Answer to it ONLY if you cannot answer F1

Another survey examines the parent’s preference in having lunch provided by the SummerIsFun Co. or lunch brought from home, based on their children’s age. Some parents might not care, any possibility is OK.

	Camp/Daycare Food (D)	Home Food (H)
Parent (Infant/Toddler) IT	50	100	150
Parent (pre-K,K) PK	85	65	150
	135	165	300

a) Compute the Marginal Probabilities and the Joint Probabilities.

Joint probabilities:	Marginal probabilities:
P(D&IT) = 16.66%	P(D) = 45%
P(D&PK = 28.33%	P(H) = 55%
P(H&IT) = 33.33%	P(IT) =50%
P(H&PK) = 21.66%	P(PK) = 50%

b) Compute: P(IT|H), P(IT or D)   

[G(28 points)]

Overall, the amount of days attended (per summer) is normally distributed around 35 days with a standard deviation of 4 days.

What’s the probability that the number of attended days will be above 28?
What percentile does an attendance of 35 days rank at?
What is the probability of attending between 33 and 39 days?
The parents with children at or below the 10%ile of number of days attended need to bring an explanatory note.   What will be the threshold of 10%?
How likely (what is the probability) is it to have the number of days attended less than 30?
Children that are in the top 15% of attendance will receive a ticket to see the DubbleCamp.   What is the minimum number of days of attendance in order to receive such a ticket?
If 49 children (49 = size of the sample) selected randomly attend the summer camp, what’s the likelihood that their mean number of attended days will be within 2 days of the population mean?

Answer 1