In October 2009, the average gas price of all US states was $1.69/gallon, with a

Question

In October 2009, the average gas price of all US states was $1.69/gallon, with a standard deviation of $0.20. Please show work to get to answer. Assume I have the zscore chart and can understand the values.

1) What percentage of states had average gas prices over $2.00/gallon.

2) What was the 9th percentile of all average gas prices/

3) Below was price did 5 states with the cheapest prices pay for gas? (hint: 5 states out of 50 means the 10th percentile)

4) What percentage of states pay, on average, between $1.50 & $1.75/gallon? In roughly how many states is the average gas price between these prices?

Explanation / Answer

a) Z = (2-1.69)/2=0.155

P(z>0.155)=0.438411

b) at 9th percentile,z =1.340755

X= 1.69+0.2*1.340755=1.958

c) At 9th percentile, z = 1.281551

X=1.69+0.2*1.281551=1.9463

d) Z1= 1.75-1.69/0.2 = 0.3

Z2=(1.5-1.69)/0.2=-0.95

P(-0.95<z<0.3)=0.4469

Number of states= 50*0.4469= roughly 23 states

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