Question

he mean gas mileage for a hybrid car is

5656

miles per gallon. Suppose that the gasoline mileage is approximately normally distributed with a standard deviation of

3.23.2

miles per gallon.​ (a) What proportion of hybrids gets over

6161

miles per​ gallon? (b) What proportion of hybrids gets

5151

miles per gallon or​ less?

left parenthesis c right parenthesis What(c) What

proportion of hybrids gets between

5959

and

6161

miles per​ gallon? (d) What is the probability that a randomly selected hybrid gets less than

4646

miles per​ gallon?

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​(a) The proportion of hybrids that gets over

6161

miles per gallon is

nothing.

​(Round to four decimal places as​ needed.)

​(b) The proportion of hybrids that gets

5151

miles per gallon or less is

nothing.

​(Round to four decimal places as​ needed.)

​(c) The proportion of hybrids that gets between

5959

and

6161

miles per gallon is

nothing.

​(Round to four decimal places as​ needed.)

​(d) The probability that a randomly selected hybrid gets less than

4646

miles per gallon is

nothing

Answer 1

a)

µ =    56                  
σ =    3.2                  
                      
P ( X ≥   61   ) = P( (X-µ)/σ ≥ (61-56) / 3.2)              
= P(Z ≥   1.563   ) = P( Z <   -1.563   ) =    0.0591   (answer)

b)

µ =    56          
σ =    3.2          
              
P( X ≤    51   ) = P( (X-µ)/σ ≤ (51-56) /3.2)      
=P(Z ≤   -1.563   ) =   0.0591   (answer)

c)

µ =    56                              
σ =    3.2                              
we need to calculate probability for ,                                  
P (   59   < X <   61   )                  
=P( (59-56)/3.2 < (X-µ)/σ < (61-56)/3.2 )                                  
                                  
P (    0.938   < Z <    1.563   )                   
= P ( Z <    1.563   ) - P ( Z <   0.938   ) =    0.9409   -    0.8257   =    0.1152

d)

µ =    56          
σ =    3.2          
              
P( X < 46   ) = P( (X-µ)/σ < (46-56) /3.2)      
=P(Z < -3.125   ) =   0.0009   (answer)