1. Following the harsh winter of 2002-2003, the interstate highways throughout V
ID: 2936573 • Letter: 1
Question
1. Following the harsh winter of 2002-2003, the interstate highways throughout Virginia suffered damage and exhibited many potholes. TheVirginia Department of Transportation reports that the number of potholes per 100 yards of interstate highway has a mean of 28 and a standard deviation of 7.5. Suppose a simple random sample of 46 100-yard stretches of interstate highways is selected and the number of potholes per 100-yard stretch determined. Based on the distribution described above, describe completely the sampling distribution of the resulting mean number of potholes per 100- yard stretch for this sample of 46 100-yard stretches of interstate highway. 2. Stocks do not always yield a positive rate of return (meaning, sometimes, investors lose money.) Last year, the rates of return were normally distributed with a mean of 3.467% and a standard deviation of 4.971%. What is the probability that a randomly selected investor will have a positive rate of return? (6 pts) a. b. What is the probability that a randomly selected group of ten investors will have an average rate of return that is positive? (6 pts)Explanation / Answer
1)as sample size is higher then 30 ; from central limit theorum sampling distribution of mean of 46 100 yard strtches of interstate highway is approimately normal with
mean =28
and std error of mean =std deviation/(n)1/2 =7.5/(46)1/2 =1.1058
2)
a)
for normal distirbution z =(X-mean)/std deviation
probability that randomely selected investor has a positive return =P(X>0) =1-P(X<0)=1-P(0-3.467)/4.971)=
=1-P(Z<-0.6974)=1-0.2428 =0.7572
b)
for sample size n=10 ; std error of mean =std deviaiton/(n)1/2 =4.971/(10)1/2 =1.5720
hence probability that average rate of return is positive =P(X>0)=1-P(X<0)=1-P(Z<(0-3.467)/1.5720)
=1-P(Z<-2.2055)=1-0.0137 =0.9863
please revert for any clarification.
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