Please show all steps and use the same numbers shown in the problem so that I ca

Question

Please show all steps and use the same numbers shown in the problem so that I can follow along easily. Thank you.

3. Michael is playing a game that involves two quarters (25 cents each), three dimes (10 cents each), one nickel (5 cents), and four pennies (1 cent each). He flips each of the coins once, and wins all of the coins that land heads up. If all of the coins are fair coins (the probability of landing heads up is ½ and the probability of landing tails up is also ½), what is the probability (to the nearest hundredth) that he will win at least fifty cents? A. 0.40 B. 0.41 C. 0.42 D. 0.46 E. 0.50

Explanation / Answer

Expected value of winning= 1/2* [ 25*2+3*10+5+4*1]= 44.5

Standard deviaton = sqrt(89*1/2]= 4.71

t= [{50-44.5}/4.71=1.16

P(t>1.16)=0.42 from t-tables

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