Use the following to answer questions 1 and 2: A commuter must pass through 5 tr

Question

Use the following to answer questions 1 and 2: A commuter must pass through 5 traffic lights on her way to work, and she will have to stop at each one that is red. Let X- the number of red lights she stops at on her way to work. She estimates the distribution for X to be as shown below: Value of X 1 2 3 4 5 Probability 0400.250.150.150.05 .On average, how many traffic lights does the commuter hit on her way to work? Include the appropriate symbol The standard deviation of the number of lights the commuter hits on her way to work uals 1.25. What are the appropriate symbol and units for this standard deviation? 3 It is estimated that chemotherapy is successful 70% of the time in curing a particular type of cancer. Suppose that 4 patients with the given type of cancer are treated and let X be the number of them that are successfully cured. 0 4 P(X x)0.01 0.08 0.27 0.40 0.24 i. What is the mean value of the number of patients that will be cured? A). 3 B). 2 C).0.2 D). 2.78 ii. What is the standard deviation of the number of patients that will be cured? A). 1.81 B). 2 C).0.934 D). 2.78

Explanation / Answer

1) expected number of traffic lights =2.2

2)std deviation =1.25

3)

(i)

mean =2.78 option D

(ii) std deviation =0.934 option C

x p(x) xP(x) x2P(X) (x-)2 (x-)2P(x) 1 0.400 0.400 0.400 1.440 0.576 2 0.250 0.500 1.000 0.040 0.010 3 0.150 0.450 1.350 0.640 0.096 4 0.150 0.600 2.400 3.240 0.486 5 0.050 0.250 1.250 7.840 0.392 total 1 = 2.20 6.400 13.200 2= 1.5600 std deviation=     =    2 = 1.2490

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