1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
vaieri [72.5K]
3 years ago
14

A new gas- and electric-powered hybrid car has recently hit the market. The distance traveled on 1 gallon of fuel is normally di

stributed with a mean of 65 miles and a standard deviation of 4 miles. Find the probability of the following events.
a. The car travels more than 70 miles per gallon.

b. The car travels less than 60 miles per gallon.

c. The car travels between 55 and 70 miles per gallon.
Mathematics
1 answer:
Doss [256]3 years ago
8 0

Answer:

a) P [ Z > 70 ]  = 0.1075  or 10.75 %

b)  P [ Z < 60 ] = 0.1038   or  10.38 %

c)  P [ 55 ≤ Z ≤ 70 ] =  0.8882   or 88.82 %

Step-by-step explanation:

Normal Distribution  μ = 65    and σ = 4

a) The probability of the car travels more than 70 miles per gallon is:

P [ Z > 70 ]  =  (Z-μ) ÷ σ  ⇒   P [ Z > 70 ] = (70-65) ÷4     P [ Z > 70 ] = 1.25

the point 1.25 corresponds at values, from left tail up to 70 so we must go and look for the area for the point 1.24 which is 0.8925. Then we have the area or probability of all cars traveling up  to 70 miles therefore  we have to subtract 1 -0,8925

P [ Z > 70 ]  = 0.1075  or 10.75 %

b)The probability of the car travels less than 60 miles per gallon is:

P [ Z < 60 ]  = ( 60 - μ ) ÷  σ ⇒  P [ Z < 60 ] = (60-65)÷ 4    P [ Z < 60 ] = -1.25

Again -1.25 corresponds to 60 miles per gallon threfore we move to the left and find for point -1.26  which area is 0.1038 so

P [ Z < 60 ] = 0.1038     10.38 %

c) P [ 55 ≤ Z ≤ 70]

For  point  Z = 70 or 1.25 (case a above)  P [ Z ≤ 70] = (70-65)÷4  

P [ Z ≤ 70] = 1.25

In this case we got the whole area from the left tail up to 1.25

P [ Z ≤ 70]  = 0.8944 (includes the area of the point from the left tail up to the point assocciated to 55 miles and for that reason we have to subtract that area)

P [ Z ≥ 55 ]  = (55-65) ÷ 4     P [ Z ≥ 55 ] = -2.5  and the area is 0.0062

So P [ 55 ≤ Z ≤ 70 ] =  0.8944 - 0.0062  = 0.8882

You might be interested in
Solve the quadratic equation by factoring:
xenn [34]
T=4,t=2 I am pretty sure that is ur answer
3 0
3 years ago
How to solve .5x+y=5
uranmaximum [27]

Answer: y is 5 and x is 1

Step-by-step explanation:

7 0
3 years ago
HELP NEEDED <br><br> Which system of linear inequalities is graphed? See screenshot!
devlian [24]
Ur graph.....u have a line that has a y int of -2....it has a slope of 3....it has a solid line...so there is no equal sign...it is shaded above the line, so it is greater then.....y > = 3x - 2

u have another line that has a y int of 2....it has a slope of -1/2....it has a solid line...so there is an equal sign in the problem...it is shaded below the line...so it is less then....
y < = -1/2x + 2
1/2x + y < = 2...multiply by 2
x + 2y < = 4

so ur answer is : y > = 3x - 2 and x + 2y < = 4...the 2nd one


3 0
3 years ago
How to make an equation out of perimeter and area
Natasha2012 [34]
Where P = perimeter, L = length, W = width, and A = area:

A = LW
P = 2(LW)

Hope this helped! :)
7 0
3 years ago
Read 2 more answers
A clothing shop is offering a 12 percent discount for senior citizens. Which equation represents the discount price?
Sliva [168]
i got what he got , If c is cost and X is the item, c=x-.12 or c=x*.88
4 0
3 years ago
Read 2 more answers
Other questions:
  • A square pyramid with a = 20 mm and b = 96 mm is shown. What is the length of side c? *Hint: you must divide the "b" by two to f
    13·2 answers
  • Y=4 what answer is correct
    6·1 answer
  • A radio is on sale for $50. If this price represents a 10% discount from the original price, what is the original price to the n
    8·1 answer
  • Susie bought 3 pies all for the same price and a snickers bar for $1 Emma bought one of same pies and spent $9 on flowers, they
    14·1 answer
  • How do you write the sum of 7 times a number is equal to 9
    5·1 answer
  • 12 more than 8.2 times n
    7·1 answer
  • Solve the exponential equation <br> 2^x+10 = 18
    15·1 answer
  • Please help me with this
    5·1 answer
  • HELPPPPPPPP 7TH GRADE MATH
    9·1 answer
  • PLZ HELP IM TIMEDDDDDDDDDDDDD Which values of a, b, and c correctly complete the division?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!