Question

A certain electric car's driving range when fully charged is approximately normally distributed, with a mean distance of 345 mi, and a standard deviation of 18mi.

A) What is the probability that a randomly selected car of that model will go more than 360 miles on a single charge?

B) Describe the sampling distribution of x-bar, the sample mean range for a random sample of 15 cars of that model.

C) What is the probability that a random sample of 15 cars of that model has a mean of more than 360 mi per charge?

D) What is the probability that a random sample of 30 cars of that model has a mean of more than 360 mi per charge?

Answer 1

Solution :

Given that ,

mean = = 345 ml

standard deviation = = 18 ml

A) P(x > 360) = 1 - p( x< 360)

=1- p P[(x - ) / < (360 - 345) / 18 ]

=1- P(z < 0.83)

Using z table,

= 1 - 0.7967

= 0.2033

B) n = 15

= = 345 ml

= / n = 18 / 15 = 4.65

C) P( > 360) = 1 - P( < 360)

= 1 - P[( - ) / < (360 - 345) / 4.65]

= 1 - P(z < 3.23)

Using z table,    

= 1 - 0.9994

= 0.0006

D) n = 30

= = 345 ml

= / n = 18 / 30 = 3.29

P( > 360) = 1 - P( < 360)

= 1 - P[( - ) / < (360 - 345) / 3.29]

= 1 - P(z < 4.56)

Using z table,    

= 1 - 1

= 0