STAT 2810 (106) Homework: Ch 17 HW #2 Score: 0 of 5 pts 17.1.53 49 of 231 You ro

Question

STAT 2810 (106) Homework: Ch 17 HW #2 Score: 0 of 5 pts 17.1.53 49 of 231 You roll a die, winning nothing if the number of spots is odd, $2 for a 2 or a 4, and $26 for a 6. a) Find the expected value and standard deviation of your prospective winnings. b) You play three times. Find the mean and standard deviation of your total winnings. c) You play 50 times. What is the probability that you win at least $330? a) What is the expected value? EX)-$ (Round to two decimal places as needed.) Enter your answer in the answer box and then click Check Answer. remainina Clear Al avascript:doExercise(9);

Explanation / Answer

for probability of odd P(X=0) =3/6 =1/2(as there are 3 odd number out of 6)

probability of 2 or 4 P(X=2) =2/6 =1/3

probability of a 6 =P(X=26)=1/6

therefore from above:

mean =5

and std deviation =9.434

b)

for three times; mean of winning =3*5=15

and std deviaiton =9.434*(3)1/2 =16.3401

c)

for playing 50 times; mean =50*5=250

and std deviaiton =9.434*(50)1/2 =66.7083

hence probability of winning at least $330 =P(X>330)=1-P(Z<330)=1-P(Z<(330-250)/66.7083)=1-P(Z<1.1993)

=1-0.8848 =0.1152

please revert for any clarification required,

x p(x) xP(x) x2P(X) (x-)2 (x-)2P(x) 0 1/2 0.000 0.000 25.000 12.500 2 1/3 0.667 1.333 9.000 3.000 26 1/6 4.333 112.667 441.000 73.500 total 1 = 5.00 114.000 475.000 2= 89.0000 std deviation=     =    2 = 9.4340

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