Question

Most electric vehicle models have a rated range between 200-250 km on a full charge Source: https://www.caa.ca/electric-vehicles/faq-electric-vehicles/. Assume that the range of a randomly selected electric vehicle has an average of 225 km and a standard deviation of 24 km.

6.1 Consider a sample of 36 electric vehicles. The distribution of the sample mean driving distance range has the following properties:

Approximate shape of distribution: ___________________________

Reason: ___________________________

Distribution mean    ___________________________

Standard error of the mean    ___________________________

6.2 Consider a sample of 36 electric vehicles. The probability that the average driving distance range is between 221 and 231 km equals:

Calculator function(s):

____________________________________     Answer: __________ (4 decimal pl)

6.3 Consider a sample of 144 electric vehicles. The distribution of the sample mean driving distance range has the following properties:

Approximate shape of distribution: ___________________________

Reason: ___________________________

Distribution mean    ___________________________

Standard error of the mean    ___________________________

6.4 What is the probability that the average driving distance range for this sample of 144 electric vehicles is greater than 228 km?

Calculator function(s):

___________________________________    Answer: ___________ (4 decimal pl)

Answer 1

Given : µ = 225 and σ = 24

6.1 (4 marks) Consider a sample of 36 electric vehicles. The distribution of the sample mean driving distance range has the following properties:

Approximate shape of distribution: Symmetric

Reason: According to sampling distribution of sample mean , the distribution of sample mean approximately follows the normal distribution with = µ and = σ/ √n

Distribution mean = 225

Standard error of the mean = 24/√36 = 4

6.2 (2 marks) Consider a sample of 36 electric vehicles. The probability that the average driving distance range is between 221 and 231 km equals:

We use TI-84 calculator to find the required probability

Press 2ND key ---> Press VARS key ---> Scroll to normalcdf and hit enter

Then plug the given values

Calculator function(s): normalcdf ( 221 , 231 , 225 , 4 )

Answer: 0.7745

6.3 (4 marks) Consider a sample of 144 electric vehicles. The distribution of the sample mean driving distance range has the following properties:

Approximate shape of distribution: Symmetric

Reason: According to sampling distribution of sample mean , the distribution of sample mean approximately follows the normal distribution with = µ and = σ/ √n

Distribution mean = 225

Standard error of the mean = 24/√144 = 2

6.4 (2 marks) What is the probability that the average driving distance range for this sample of 144 electric vehicles is greater than 228 km?

Calculator function(s): normalcdf( 228 , 99999 , 225 , 2 )

Answer: 0.0668