Urban planners will use electronic traffic counters to count

Urban planners will use electronic traffic counters to count the number of vehicles that travel on a specific road. This information can be used to identify roads that need to be improved or expanded based on traffic needs. Suppose that, from historical studies. Duncan Road in Kent Count) averages 2.165 vehicles per day with a standard deviation of 4H5 vehicles per day. A traffic counter was used on this road on 33 days that were randomly selected. What is the probability that the sample mean is less than 2.000 vehicles per day? What is the probability that the sample mean is more than 2.200 Vehicles per day? What is the probability that the sample mean is between 2.100 and 2.300 vehicles per day? Suppose the sample mean was 2.400 vehicles per day. Does this result support the stated population mean for this road?

Solution

(a) P(xbar<2000) = P((xbar-mean)/(s/vn) <(2000-2165)/(485/sqrt(33)))

=P(Z<-1.95) = 0.0256 (from standard normal table)

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(b)P(xbar>2200) = P(Z>(2200-2165)/(485/sqrt(33)))

=P(Z>0.41) = 0.3409 (from standard normal table)

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(c)P(2100<xbar<2300)

=P((2100-2165)/(485/sqrt(33)) <Z< (2300-2165)/(485/sqrt(33)))

=P(-0.77<Z<1.60)

=0.7246 (from standard normal table)

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(d)P(xbar>2400) = P(Z> (2400-2165)/(485/sqrt(33)))

=P(Z>2.78) = 0.0027(from standard normal table)

Since the probability is less than 0.05, this result does not support the stated population mean for this road