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Dr. Quack Dr. Quack is a physician with a unique approach to medicine. She believes all illness can be attributed to just 10 different causes. The table below lists Quack\'s diagnoses, treament costs, and the probability each patient has a particular affliction. Use this information to answer the following items: What Is the probability the cost will be at least $230? What is the E(x) for this distribution? What Is the standard deviation for this distribution? What is the probability the cost will be less than $110? What is the probability the cost will be at least $150 but less than $190?

Solution

Q1 P(x>=230)=1-P(x<230)

we sum the probabilites for values less than 230 and then subtract with 1.

=1-0.639=0.361

Q2: E(X)=sum(X*P(X))

E(X)=355.268

Q3 P(X<110)

sum probabilites for values <110

P(X<110)=0.075

Q4 P(150<=X<190)= sum probabilites form 150 to less than 190.

P(150<=X<190)=0.196

x	p(x)	x*P(X)
68	0.019	1.292
72	0.021	1.512
100	0.035	3.5
126	0.048	6.048
142	0.066	9.372
166	0.088	14.608
188	0.108	20.304
192	0.116	22.272
220	0.138	30.36
246	1	246
		355.268