Question
In: Statistics and Probability
The mpg (miles per gallon) for all cars has a normal distribution with mean 100 km/L...
The mpg (miles per gallon) for all cars has a normal distribution with mean 100 km/L and standard deviation of 15 km/L
a) Calculate the probability that any randomly selected car has an amount of mpg greater than 120 km/L.
b) Calculate the probability that any randomly selected car has an amount of mpg less than 95 km/L.
c) Calculate the probability that any randomly selected car has an amount of mpg between 93 km/L and 110 km/L.
d) A car is identified as a “best quality” if it is included in the top 2% of all mpgs. Find the minimum mpg needed to be qualified as “best quality”.
Solutions
orchestra answered 2 years agoRelated Solutions
1. (No computer output is accepted) The mpg (miles per gallon) for all cars has a...
1. (No computer output is accepted) The mpg (miles per gallon)
for all cars has a normal distribution with mean 100 km/L and
standard deviation of 15 km/L.
a) Calculate the probability that any randomly selected car has
an amount of mpg greater than 120 km/L.
b) Calculate the probability that any randomly selected car has
an amount of mpg less than 95 km/L.
c) Calculate the probability that any randomly selected car has
an amount of mpg between 93...
Suppose that the miles-per-gallon (mpg) rating of passenger cars is normally distributed with a mean and...
Suppose that the miles-per-gallon (mpg) rating of passenger cars
is normally distributed with a mean and a standard deviation of
32.6 and 4.9 mpg, respectively. [You may find it useful to
reference the z table.] a. What is the probability that a randomly
selected passenger car gets more than 36 mpg? (Round “z” value to 2
decimal places, and final answer to 4 decimal places.) b. What is
the probability that the average mpg of two randomly selected
passenger cars...
Suppose that the miles-per-gallon (mpg) rating of passenger cars is normally distributed with a mean and...
Suppose that the miles-per-gallon (mpg) rating of passenger cars
is normally distributed with a mean and a standard deviation of
31.6 and 4.9 mpg, respectively.
a. What is the probability that a randomly
selected passenger car gets more than 35 mpg? (Round
“z” value to 2 decimal places, and final answer to 4
decimal places.)
b. What is the probability that the average mpg of
two randomly selected passenger cars is more than 35 mpg?
(Round “z” value to 2...
Suppose that the miles-per-gallon (mpg) rating of passenger cars is normally distributed with a mean and...
Suppose that the miles-per-gallon (mpg) rating of passenger cars
is normally distributed with a mean and a standard deviation of
35.9 and 2.5 mpg, respectively. [You may find it useful to
reference the z table.]
a. What is the probability that a randomly selected passenger
car gets more than 37 mpg?
b. What is the probability that the average mpg
of three randomly selected passenger cars is more than 37 mpg?
(Round “z” value to 2 decimal places, and final...
Suppose that the miles-per-gallon (mpg) rating of passenger cars is normally distributed with a mean and...
Suppose that the miles-per-gallon (mpg) rating of passenger cars
is normally distributed with a mean and a standard deviation of
30.9 and 2.7 mpg, respectively. [You may find it useful to
reference the z table.]
a. What is the probability that a randomly
selected passenger car gets more than 32 mpg? (Round
“z” value to 2 decimal places, and final answer to 4
decimal places.)
b. What is the probability that the average mpg
of four randomly selected passenger cars...
A car manufacturer claims that the miles per gallon (mpg) of all its midsize cars can...
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).
What proportion of cars have miles per gallon less than 31.2
[P(x ≤31.2 mpg)]?
What proportion of cars will have miles per gallon greater than
36 [P(x ≥36 mpg)]?
What proportion of cars will have miles per gallon less than
30[P(x ≤30 mpg)]?
What proportion of cars will have miles per gallon between 32
and...
The fuel consumption, in miles per gallon, of all cars of a particular model has a...
The fuel consumption, in miles per gallon, of all cars of a
particular model has a mean of 25 and a standard deviation of 2.
The population distribution can be assumed as normal. A random
sample of these cars is taken.
a. Find the probability that the sample mean fuel consumption
will be fewer than 24 miles per gallon if (i) a sample of 1
observation is taken, (ii) a sample of 4 observations if taken and
(iii) a sample...
Suppose that the miles-per-gallon (mpg) rating of passenger cars is a normally distributed random variable with...
Suppose that the miles-per-gallon (mpg) rating of passenger cars
is a normally distributed random variable with a mean and standard
deviation of 33.8 and 3.5 mpg, respectively.
a. What is the probability that a randomly selected passenger
car gets more than 35mpg?
b. a random sample of twenty-five passenger cars is selected.
Denote Xbar as the sample average mpg of this twenty-five. What is
the mean and standard deviation of Xbar?
c. What is the probability that the average mpg...
Below is a frequency distribution for the estimated miles per gallon (MPG) for 530 different models...
Below is a frequency distribution for the estimated miles per
gallon (MPG) for 530 different models of American-made cars.
American-Made Cars
MPG
Frequency
7 - 12
57
13 - 18
177
19 - 24
167
25 - 30
77
31 - 36
40
37 - 42
12
(a) Identify the following
class midpoints (enter as a comma-separated list)
class boundaries (enter as a comma-separated list)
class width
(b) Create a relative frequency table from the frequency
table.
American-Made Cars
MPG...
Some manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones....
Some manufacturers claim that non-hybrid sedan cars have a lower
mean miles-per-gallon (mpg) than hybrid ones. Suppose that
consumers test 21 hybrid sedans and get a mean of 32 mpg with a
standard deviation of 7 mpg. Thirty-one non-hybrid sedans get a
mean of 21 mpg with a standard deviation of four mpg. Suppose that
the population standard deviations are known to be six and three,
respectively. Conduct a hypothesis test at the 5% level to evaluate
the manufacturers claim....
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