A car manufacturer claims that the miles per gallon (mpg) of all its midsize cars can be modeled with a normal model with N(33, 1.70).

1. What proportion of cars have miles per gallon less than 31.2 [P(x ≤31.2 mpg)]?

2. What proportion of cars will have miles per gallon greater than 36 [P(x ≥36 mpg)]?

3. What proportion of cars will have miles per gallon less than 30[P(x ≤30 mpg)]?

4. What proportion of cars will have miles per gallon between 32 and 35 [P(32 mpg ≤x ≤35 mpg)]?

5. How many miles per gallon do the top 10% of the midsize cars have?

Speeding on the I-5. Suppose the distribution of passenger vehicle speeds traveling on the Interstate 5 Freeway (I-5) in California is nearly normal with a mean of 70.4 miles/hour and a standard deviation of 4.5 miles/hour. Round all answers to four decimal places.

1. What proportion of passenger vehicles travel slower than 80 miles/hour?

2. What proportion of passenger vehicles travel between 73 and 79 miles/hour?

3. How fast do the fastest 8% of passenger vehicles travel?  miles/hour

4. Suppose the speed limit on this stretch of the I-5 is 70 miles/hour. Approximately what proportion of the passenger vehicles travel above the speed limit on this stretch of the I-5?

1.- Find the following probabilities. (a) P(Z > 1.4)    (b) P(−1 < Z < 1) (c) P(Z < −1.49)

2.- Find (a) Z0.03 (b) Z0.07

3.- The distance that a Tesla model 3 can travel is normally distributed with a mean of 260 miles and a standard deviation of 25 miles.

(a) What is the probability that a randomly selected Tesla model 3 can travel more than 310 miles?

(b) What is the probability that a randomly selected Tesla model 3 can travel less than 300 miles?

(c) What is the probability that a randomly selected Tesla model 3 can travel between 235 miles and 310 miles?

(d) Now, suppose that you pick a random sample of 9 Tesla model 3. What is the probability that the sample mean will be more than 250 miles.

(e) Does the Central Limit Theorem applies in Part (d)? Explain.

or a new type of​ tire, a racing car team found the average distance a set of tires would run during a race is 166 ​miles, with a standard deviation of 14 miles. Assume that tire mileage is independent and follows a Normal model. ​a) If the team plans to change tires twice during a​ 500-mile race, what is the expected value and standard deviation of miles remaining after two​ changes? ​b) What is the probability they​ won't have to change tires a third time​ (and use a fourth set of​ tires) before the end of a 500 mile​ race? ​a) The expected value for miles remaining is 168 miles. ​(Type an integer or decimal rounded to three decimal places as​ needed.) The standard deviation for miles remaining is 19.799 miles. ​(Type an integer or decimal rounded to three decimal places as​ needed.) ​b) The probability they​ won't have to change tires a third time is ​(Type an integer or decimal rounded to three decimal places as​ needed.)

Prior to adjustment at the end of the year, the balance in Trucks is $301,820 and the balance in Accumulated Depreciation—Trucks is $102,720. Details of the subsidiary ledger are as follows:

A. Determine the depreciation rates per mile and the amount to be credited to the accumulated depreciation section of each of the subsidiary accounts for the miles operated during the current year.

.31 x 7700 = 2387, but that is not the answer. How do I find it?

A fisherman is in a row boat on a lake 2 miles form shore when he catches a huge fish. He wants to show the fish to his buddies in a tavern 3 miles down the straight shore. He can row 5 miles an hour and run 13 miles per hour. To what point on the shore should he row to get to the tavern as quickly as possible?

Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. Then find the mean, variance, and standard deviation.

Please provide an aswer and reference(s) to the question below from a classmate. Thank you in advance!

Class,

I am having a problem with the following problem:

A certain brand of automobile tire has a mean life span of 39,000 miles and a standard deviation of 2,250 miles.​ (Assume the life spans of the tires have a​ bell-shaped distribution.)

For the life span of 34,000 miles, z-score is = 34,000 x 39,000 = -2.22

2,250

For the life span of 34,000 miles, z-score is = 38,000 x 39,000 = -0.44

2,250

For the life span of 34,000 miles, z-score is = 31,000 x 39,000 = -3.56

2,250

The following is the part I am having trouble with:

The life spans of three randomly selected tires are 34,500 miles, 43,500 miles, and 39,000

miles. Using the empirical​ rule, find the percentile that corresponds to each life span:

1. The life span 34,500 miles corresponds to the ___th percentile?

2. The life span 43,500 miles corresponds to the ___th percentile?

3. The life span 39,000 miles corresponds to the ___th percentile?

I have found in the text in Chapter 2, p.88 where it talks about Empirical Rules and Bell-Shaped Distribution. I did find that number 3 is "50"th percentile, as it is also the mean value in this problem set. Numbers 1 and 2 I am having an issue calculating. Any help from my battle buddies would be outstanding. Thank you in advance!

Reference:

Larson, R. & Farber, B. (2015). Elementary Statistics: picturing the world. 6th edition.

Scott placed a business auto in service on January 1 2016 and drove it 5629 miles for business 3377 miles for commuting and 6755 miles for non-business service what about can he deduct on his taxes