The average speed of all vehicles on a highway is mu = 64 mph with a standard de

Question

The average speed of all vehicles on a highway is mu = 64 mph with a standard deviation of sigma = 5 mph. A random sample of 20 vehicles is clocked. What is the probability that the sample mean will exceed 66 mph? 0.0525 0.0404 0.0367 0.0220 In the previous question what fraction of sample means from samples of n = 20 vehicles fall within plusminus 1 mph from the population mean speed? 0.6266 0.6528 0.6922 0.7286 If you doubled the sample size in the previous question, what fraction of the sample means would fall within plusminus 1 mph from the population mean speed? 0.7108 0.7924 0.8262 0.8558 In the previous question where n = 40, the middle interval which includes the 95% of the mean speed from samples of n = 40 vehicles is, 61.63 66.37 62.45 65.55 63.05 64.95 63.37 64.63

Explanation / Answer

Q5.

Mean ( u ) =64
Standard Deviation ( sd )= 5/ Sqrt(n) = 1.118
Number ( n ) = 20
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X > 66) = (66-64)/5/ Sqrt ( 20 )
= 2/1.118= 1.7889
= P ( Z >1.7889) From Standard Normal Table
= 0.0367

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