Question

A major U.S. automaker has determined that the city mileage for its new hybrid gas/electric model...

A major U.S. automaker has determined that the city mileage for its new hybrid gas/electric model is normally distributed with a mean equal to 52 miles per gallon (μ = 52) and a standard deviation of 3.7 mpg (σ = 3.7).

A. What is the probability a vehicle would get less than 50 miles per gallon, i.e., P(x < 50)?
Enter your response rounded to 3 decimals, in the format 0.123 with no other text or symbols.

B. What is the probability a vehicle would get more than 60 miles per gallon, i.e., P(x > 60)?
Enter your response rounded to 3 decimals, in the format 0.123 with no other text or symbols.

C. What vehicle mileage is at the 90th percentile?
Enter your response rounded to 1 decimal, in the format 1.2 with no other text or symbols.

Homework Answers

Answer #1

Solution :

Given that ,

mean = = 52

standard deviation = = 3.7

A)

P(x < 50) = P((x - ) / < (50 - 52) / 3.7)

= P(z < -0.54)

Using standard normal table,

P(x < 50) = 0.2946 = 0.295

Probability = 0.295

B)

P(x > 60) = 1 - P(x < 60)

= 1 - P((x - ) / < (60 - 52) / 3.7)

= 1 - P(z < 2.162)

= 1 - 0.9847

= 0.0153

P(x > 60) = 0.0153

Probability = 0.0153

C)

P(Z < z) = 90%

P(Z < 1.28) = 0.90

z = 1.28

Using z-score formula,

x = z * +

x = 1.28 * 3.7 + 52 = 56.7

90th percentile = 56.7

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
We expect a car’s highway gas mileage to be related to its city gas mileage (in...
We expect a car’s highway gas mileage to be related to its city gas mileage (in mpg). Data for all 12091209 vehicles in the government’s 2016 Fuel Economy Guide give the regression line highway mpg=7.903+(0.993×city mpg)highway mpg=7.903+(0.993×city mpg) for predicting highway mileage from city mileage. (a) What is the slope of this line? (Enter your answer rounded to three decimal places.) slope: What does the numerical value of the slope tell you? Highway gas mileage increases with city gas mileage...
We expect a car’s highway gas mileage to be related to its city gas mileage (in...
We expect a car’s highway gas mileage to be related to its city gas mileage (in mpg). Data for all 1209 vehicles in the government’s 2016 Fuel Economy Guide give the regression line highway mpg=7.903+(0.993×city mpg) for predicting highway mileage from city mileage. (a) What is the slope of this line? (Enter your answer rounded to three decimal places.) slope: What does the numerical value of the slope tell you? On average, highway mileage increases by 0.993 mpg for each...
We expect a car’s highway gas mileage to be related to its city gas mileage (in...
We expect a car’s highway gas mileage to be related to its city gas mileage (in mpg). Data for all 1209 vehicles in the government’s 2016 Fuel Economy Guide give the regression line highway mpg=7.903+(0.993×city mpg) for predicting highway mileage from city mileage. (a) What is the slope of this line? (Enter your answer rounded to three decimal places.) slope: What does the numerical value of the slope tell you? On average, highway mileage decreases by 0.993 mpg for each...
A new car that is a gas- and electric-powered hybrid has recently hit the market. The...
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 60 miles and a standard deviation of 6 miles. Find the probability of the following events: A. The car travels more than 63 miles per gallon. Probability = B. The car travels less than 52 miles per gallon. Probability = C. The car travels between 52 and 66 miles per...
We expect a car's highway gas mileage to be related to its city gas mileage (in...
We expect a car's highway gas mileage to be related to its city gas mileage (in miles per gallon, mpg). Data for all 1137 vehicles in the government's 2013 Fuel Economy Guide give the regression line highway mpg = 6.785 + (1.033 × city mpg) for predicting highway mileage from city mileage. (a) What is the slope of this line? (Enter your answer to three decimal places.) ____mpg Say in words what the numerical value of the slope tells us....
We expect a car's highway gas mileage to be related to its city gas mileage (in...
We expect a car's highway gas mileage to be related to its city gas mileage (in miles per gallon, mpg). Data for all 1137 vehicles in the government's Fuel Economy Guide give the regression line highway mpg = 6.785 + (1.033 * city mpg) for predicting highway mileage from city mileage. (a) What is the slope of this line? (Enter your answer to three decimal places.) mpg Say in words what the numerical value of the slope tells us. Highway...
A new car that is a gas- and electric-powered hybrid has recently hit the market. The...
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 60 miles and a standard deviation of 7 miles. Find the probability of the following events: A. The car travels more than 65 miles per gallon. Probability = B. The car travels less than 54 miles per gallon. Probability = C. The car travels between 52 and 67 miles per...
A new car that is a gas- and electric-powered hybrid has recently hit the market. The...
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 60 miles and a standard deviation of 5 miles. Find the probability of the following events: Be sure to use at least 4 decimals of accuracy in your answers: A) The car travels more than 65 miles per gallon. B) The car travels between 53 and 64 miles per gallon.
A new car that is a gas- and electric-powered hybrid has recently hit the market. The...
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 7 miles. Find the probability of the following events: A. The car travels more than 53 miles per gallon. Probability = B. The car travels less than 47 miles per gallon. Probability = C. The car travels between 42 and 58 miles per...
A certain model of automobile has its gas mileage (in miles per gallon, or mpg) normally...
A certain model of automobile has its gas mileage (in miles per gallon, or mpg) normally distributed, with a mean of 32 mpg and a standard deviation of 4 mpg. Find the probability that a car selected at random has the following gas mileages. (Round your answers to four decimal places.) (a) less than 26 mpg (b) greater than 34 mpg (c) between 30 and 34 mpg
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT