Question

13.NormalDistribution 1: Problem 3

13.NormalDistribution 1: Problem 3 Previous Problem Problem List Next Problem (1 point) A new car that is a gas- and electric-powered hybrid has recently hit the market. The distance travelled on 1 gallon of fuel is normally distributed with a mean of 50 miles and a standard deviation of 6 miles. Find the probability of the following events: A. The car travels more than 53 miles per gallon. Probability = 0.30854 B. The car travels less than 46 miles per gallon. Probability = 0.25463 C. The car travels between 42 and 58 miles per gallon. Probability = 0.81648

Answer 1

Solution :

Given that ,

mean = $\mu$ = 50

standard deviation = $\sigma$ = 6

a.

P(x > 53) = 1 - P(x < 53)

= 1 - P[(x - $\mu$ ) / $\sigma$ < (53 - 50) / 6)

= 1 - P(z < 0.5)

= 1 - 0.6915

= 0.3085

Probability = 0.3085

b.

P(x < 46) = P[(x - $\mu$ ) / $\sigma$ < (46 - 50) / 6]

= P(z < -0.67)

= 0.2514

Probability = 0.2514

c.

P(42 < x < 58) = P[(42 - 50)/ 6) < (x - $\mu$ ) /$\sigma$  < (58 - 50) / 6) ]

= P(-1.33 < z < 1.33)

= P(z < 1.33) - P(z < -1.33)

= 0.9082 - 0.0918

= 0.8164

Probability = 0.8164