My Notes Ask Your Teacher Dylan asks for his lunch money every day from his moth

Question

My Notes Ask Your Teacher Dylan asks for his lunch money every day from his mother. There is an 80% chance she has money to give him and if so, he gets $5. However, if she does not have money Dylan has to give her $2. whether Dylan gets $5 or gives out $26s independent from day to day. Let x equal the number of times Dylan gets money during a 5-day week. Let w·the total amount he gets/gives for lunch in a week. (When he gives money just make the amount negative a. As a function of x, what is w b. What is the expected value of x? c. What is the expected value of w? d. What is the probability thatS7 e. What is the probability that x >1? f. What is the standard deviation of ? g. What is the standard deviation of w? h. What is the probabiaty that W10 i What is the probabiity that w is within & standard deviation of its expected value? Add any comments below

Explanation / Answer

a. W = Earning for dylan - loss for dylan

W = 5X - 2 *(5-X) = 5X - 10 + 2X = 7X - 10

b. E(X) = 5 * 0.8 = 4

c . E(W) = E(7X -10) = 7 * E(X) - 10 = 28- 10 = 18

d. P(X =5) = 5C5 (0.8)5 = 0.3277

e. P(X >1) = 1 - P(0) - P(1) = 1 -  5C0(0.2)5  -  5C1 (0.2)4  (0.8)

= 0.9933

f. STD(X) = sqrt(5 * 0.8 * 0.2) = 0.8944

g. STD(W) = STD(7X -10) = 7 * STD(X) = 7 * 0.8944 = 6.261

h. P(W >10) , it will occur for X >=3

so, Pr(X >=3) = Pr (X = 3) + Pr(X =4) + Pr(X =5)

= 0.942

i. w within 1 standard deviation of its expected value.

LCL = 18 - 6.261 = 11.74

UCL = 18 + 6.261 = 24.261

that mweans W can be only 18

Pr(W = 18) = Pr( X = 4) = 5C4 (0.8)4 (0.2)2 = 0.4096

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