Question

1. Based on tests of the Chevrolet Cobalt, engineers have found that the miles per gallon in highway driving are normally distributed, with a mean of 32 mpg and a standard deviation of 3.5 mpg. Include a sketch for each part.

a. What is the probability that a randomly selected Cobalt gets more than 34 mpg?

b. Ten Cobalts are randomly selected. What is the probability that the mean is more than 34 mpg?

Answer 1

Solution :

a.

P(x > 34) = 1 - P(x < 34)

= 1 - P[(x - ) / < (34 - 32) / 3.5)

= 1 - P(z < 0.5714)

= 1 - 0.7161

= 0.2839

Probability = 0.2839

b.

= / n = 3.5 / 10 = 1.1068

P( > 34) = 1 - P( < 34)

= 1 - P[( - ) / < (34 - 32) / 1.1068]

= 1 - P(z < 1.8070)

= 1 - 0.9646

= 0.0354

Probability = 0.0354