Question

The EPA Fuel Economy Estimates for automobile models tested recently predicted a mean of 24.8 Miles...

The EPA Fuel Economy Estimates for automobile models tested recently predicted a mean of 24.8 Miles per gallon, with a standard deviation of 6.2 miles per gallon. Assume that a normal model applies. Find the probability that a randomly selected automobile will average

1 a) Less than 20 Miles per gallon

1 b) More than 14 Miles per gallon

1c ) Between 25 and 30 miles per gallon

Homework Answers

Answer #1

Solution :

Given that ,

mean = = 24.8

standard deviation = = 6.2

a) P(x < 20) = P[(x - ) / < (20 - 24.8) /6.2 ]

= P(z < -0.77)

= 0.2206

Probability = 0.2206

b) P(x > 14) = 1 - P(x < 14)

= 1 - P[(x - ) / < (14 - 24.8) /6.2 )

= 1 - P(z < -1.74)

= 1 - 0.0409 = 0.9591

Probability = 0.9591

c) P(25 < x < 30) = P[(25 - 24.8)/ 6.2 ) < (x - ) /  < (30 - 24.8) / 6.2) ]

= P(0.03 < z < 0.84)

= P(z < 0.84) - P(z < 0.03)

= 0.7995 - 0.512 = 0.2875

Probability = 0.2875

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
The Environmental Protection Agency (EPA) fuel economy estimates for automobile models tested recently predicted a mean...
The Environmental Protection Agency (EPA) fuel economy estimates for automobile models tested recently predicted a mean of 24.8 miles per gallon, with a standard deviation of 6.2 miles per gallon. Assume that a Normal model applies. Find the probability that a randomly selected automobile will average: 1. Less than 20 miles per gallon. 2. More than 30 miles per gallon. 3. Between 25 and 32 miles per gallon
The Environmental Protection Agency (EPA) fuel economy estimates for automobile models tested recently predicted a mean...
The Environmental Protection Agency (EPA) fuel economy estimates for automobile models tested recently predicted a mean of 24.8 mpg and a standard deviation of 6.2 mpg for highway driving. Assume that a Normal model can be applied. a) Draw the model for auto fuel economy. Clearly label it, showing what the 68-95-97 Rule predicts. Use StatCrunch, Excel, or Minitab. b) In what interval would you expect the central 68% of autos to be found? c) About what percent of autos...
The Environmental Protection Agency measures a mean gas mileage for recently tested cars as 24.8 mpg...
The Environmental Protection Agency measures a mean gas mileage for recently tested cars as 24.8 mpg with a standard deviation of 6.2 mpg. The dataset on Fuel economy in StatCrunch gives an average of 24.2 mpg with a standard deviation of 6.5 mpg. Joe’s car is estimated at 30 mpg. (a) Calculate the z-scores to find the relative tab at both sources (the Exercise and the Dataset). (b) Relative to the other cars, with which source will Joe have the...
Suppose that you work for the EPA and, given the current fuel issues, are interested in...
Suppose that you work for the EPA and, given the current fuel issues, are interested in the gas mileage of their new car the “Flash.” The manufacturers claim that the realized gas mileage for any individual car follows a normal distribution with mean of 32 and variance of 9. You randomly sample 36 of these cars to test out their mileage and find that they averaged 30 miles per gallon among them. a. What is the probability that a randomly...
the Environmental Protection Agency measures a mean gas mileage for recently tested cars as 24.8 mpg...
the Environmental Protection Agency measures a mean gas mileage for recently tested cars as 24.8 mpg with a standard deviation of 6.2 mpg. The dataset on Fuel economy in StatCrunch gives an average of 24.2 mpg with a standard deviation of 6.5 mpg. Joe’s car is estimated at 30 mpg. (a)   Calculate the z-scores to find the relative tab at both sources (the Exercise and the Dataset). (b)   Relative to the other cars, with which source will Joe have the...
Two models of a popular pick-up truck are tested for miles per gallon (mpg) gasoline consumption....
Two models of a popular pick-up truck are tested for miles per gallon (mpg) gasoline consumption. The Pacer model was tested using a random sample of n1=9 trucks and the sample mean of 27.3 mpg with sample standard deviation s1=6.2 mpg. The Road Runner model was tested using a random sample of n2=14 trucks. The sample mean was 22.5 mpg with sample standard deviation s2=6.8 mpg. Does this indicate that the population mean gasoline consumption for the Pacer is higher...
Assume that fuel economy follows a normal distribution with mean of 24 mpg (miles per gallon)...
Assume that fuel economy follows a normal distribution with mean of 24 mpg (miles per gallon) and a standard deviation of 6 mpg. (a) In what interval would you expect the central 68% of autos to be found? (b) What percent of autos should get more than 30 mpg? (c) What gas mileage corresponds to the worst 2.5% of all cars?
A consumer research group is interested in testing an automobile manufacturer's claim that a new economy...
A consumer research group is interested in testing an automobile manufacturer's claim that a new economy model will travel at least 27 miles per gallon of gasoline (H 0:   27). With a .02 level of significance and a sample of 40 cars, what is the rejection rule based on the value of x for the test to determine whether the manufacturer's claim should be rejected (to 2 decimals)? Assume that x is 5 miles per gallon. Reject H 0 if x...
A consumer research group is interested in testing an automobile manufacturer's claim that a new economy...
A consumer research group is interested in testing an automobile manufacturer's claim that a new economy model will travel at least 27 miles per gallon of gasoline (H 0:   27). a. With a .02 level of significance and a sample of 40 cars, what is the rejection rule based on the value of 'x bar ' for the test to determine whether the manufacturer's claim should be rejected (to 2 decimals)? Assume that population standard deviation is 6 miles per gallon....
A consumer research group is interested in testing an automobile manufacturer's claim that a new economy...
A consumer research group is interested in testing an automobile manufacturer's claim that a new economy model will travel at least 26 miles per gallon of gasoline (H 0:   26). With a .02 level of significance and a sample of 30 cars, what is the rejection rule based on the value of  for the test to determine whether the manufacturer's claim should be rejected (to 2 decimals)? Assume that  is 6 miles per gallon. Reject H 0 if  is Selectless than or equal togreater...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT