The Energy Information Administration reported that the mean retail price per ga

Question

The Energy Information Administration reported that the mean retail price per galon of regular grade sasolire wa $3,60 Suppose that the standard dev/ation was $.10 and that the $3.60 Suppoe that the standard deviation was $.10 and that the retal price per galion has a bell-shaped distribution a. what percentage of regular grade gasoline sold between $3.40 and $3.80 per gaton (to 1 deamal b. What percentage of reguliar grade oasoline sold between $3.40 and 83.70 pr galion toem? c what percentage of regular grade gasecline soid for more than $3.70 per galon (to 1 decimaly

Explanation / Answer

Mean= $3.60 and std= $.10

a) Percentage of regular grade gasoline between $3.4 and $3.80 is

Since =3.60 and =0.10 we have:

P ( 3.40<X<3.80 )=P ( 3.403.60< X<3.803.60 )=P ( (3.403.60)/.10<(X)/<(3.803.60)/.10)

Since Z=(x)/ , (3.403.60)/.10=2 and (3.803.60)/.10=2 we have:

P ( 3.40<X<3.80 )=P ( 2<Z<2 )

Use the standard normal table to conclude that:

P ( 2<Z<2 )=0.9544= 95.4%

b) Since =3.60 and =0.10 we have:

P ( 3.40<X<3.70 )=P ( 3.403.60< X<3.703.60 )=P (( 3.403.60)/.10<(X)/<(3.703.60)/.10)

Since Z=(x)/ , (3.403.60)/.10=2 and (3.703.60)/.10=1 we have:

P ( 3.40<X<3.70 )=P ( 2<Z<1 )

Use the standard normal table to conclude that:

P ( 2<Z<1 )=0.8185= 81.8%

c)

Since =3.60 and =0.10 we have:

P ( X>3.70 )=P ( X>3.703.60 )=P ((X)/>(3.703.60)/.10)

Since Z=(x)/ and (3.703.60)/.10=1 we have:

P ( X>3.70 )=P ( Z>1 )

Use the standard normal table to conclude that:

P (Z>1)=0.1587= 15.9%

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