U 0ur0 01 T1Ul uyling?3marks] 3. The completion times for Algebra Adventure have

Question

U 0ur0 01 T1Ul uyling?3marks] 3. The completion times for Algebra Adventure have a mean of 48 hours and a standard deviation of 12 hours. You may assume that these times follow a Normal sn distribution a) Calculate the probability that a gamer selected at random takes less than 30 b) Calculate the probability that a gamer selected at random takes between 30 [2 marks] hours to complete it. and 45 hours to complete it. What is the probability that three gamers selected at random have a total [3 marks] [3 marks] c) Calculate the lower quartile of time taken to complete it. d) completion time for AA of less than 102 hours? [4 marks]

Explanation / Answer

Solution:

Mean =48

SD = 12

Solution(1)

P(xbar<30)

Z =(30-48/12) =-18/12 =-1.5

So from z table we found that

P(xbar<30) =0.0668 or 6.668%

Solution(2)

P(30<xbar<45)=p(xbar<45)-p(xbar<30)

Z =45-48/12 =-0.25

So P(30<xbar<45) = 0.4013-0.0668 = 0.3345 or 33.45%

Solution(3)

Lower quartile contains 25% of data so

P=0.25

Here Z value is -0.67

So -0.67 =Xbar -48)/12

-8.04 =Xbar-48

Xbar = 39.96

So lower quartile is 39.96

Solution(4)

Xbar =102/3 = 34

Mean =48

So Z = (34-48)/12/sqrt(3) = -14*1.75/12 = -1.1666*1.75 =-2.04

From z table we found that

P(xbar<34 or total of 102) = 0.0207 or 2.07%

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