The mean gas mileage for a hybrid car is 5656 miles per gallon. Suppose that the

Question

The 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 of3.33.3 miles per gallon.? (a) What proportion of hybrids gets over 6262 miles per? gallon? (b) What proportion of hybrids gets 5050 miles per gallon or? less? left parenthesis c right parenthesis What(c) Whatproportion of hybrids gets between 5757 and 6161 miles per? gallon? (d) What is the probability that a randomly selected hybrid gets less than 4545 miles per? gallon?

Explanation / Answer

solution :

Given that mean ? = 56 , standard deviation ? = 3.3

(a) P(x > 62) = P((x - ?)/? > (62 - 56)/3.3)

= P(Z > 1.8182)

= 0.0344

(b) P(x < 50) = P((x - ?)/? < (50 - 56)/3.3)

= P(Z < -1.8182)

= 0.9656

(c) P(57 < x < 61) = P((57 - 56)/3.3 < Z < (61 - 56)/3.3)

= P(0.3030 < Z < 1.5152)

= 0.3178

(d) P(x < 45) = P((x - ?)/? < (45 - 56)/3.3)

= P(Z < -3.3333)

= 0.0004

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