13. The viscosity of a fluid can be measured in an experiment by dropping a smal

Question

13. The viscosity of a fluid can be measured in an experiment by dropping a smal ball into a calibrated tube containing the fluid and observing the random variable X, the time it takes for the ba to drop the measured distance. Assume that X is normally distributed with a mean of 20 seconds and a standard deviation of 0.5 second for a particular type of liquid (a) What is the standard deviation of the average time of 40 experiments? (b) What is the probability that the average time of 40 experiments will exceed 20.1 seconds? (c) Suppose the experiment is repeated only 20 times. What is the probability that the average value of X will exceed 20.1 seconds? Due: N/A 17 Fall MATH 3020 Exam 2 Review (d) Is the probability computed in part (b) greater than or less than the probability computed in part (c)? Explain why this inequality occurs

Explanation / Answer

a) std deviation of average time =std deviation/(n)1/2 =0.5/(40)1/2 =0.0791

b)probability that sample mean exceed 20.1=P(X>20.1) =1-P(X<20.1)=1-P(Z<(20.1-20)/0.0791)=1-P(Z<1.2649)

=1-0.8970 =0.1030

c)) std deviation of average time =std deviation/(n)1/2 =0.5/(20)1/2 =0.1118

probability that sample mean exceed 20.1=P(X>20.1) =1-P(X<20.1)=1-P(Z<(20.1-20)/0.1118)=1-P(Z<0.8944)

=1-0.8144 =0.1855

d)

as we can see that in part b) due to higher sample size ; sample mean value should be close to its population parameter due to law of large numbers and should show low variability. Therefore for sample size probability to be higher then 20.1 should be less in comparison to sample size of 20.

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