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
Mariulka [41]
3 years ago
9

A gasoline tank for a certain car is designed to hold 14.0 gal of gas. Suppose that the variable x = actual capacity of a random

ly selected tank has a distribution that is well approximated by a normal curve with mean 14 gal and standard deviation 0.2 gal. (Round all answers to four decimal places.)
(a) What is the probability that a randomly selected tank will hold at most 13.7 gal?

P(x ? 13.7) =

(b) What is the probability that a randomly selected tank will hold between 13.4 and 14.3 gal?

P(13.4 ? x ? 14.3) =

(c) If two such tanks are independently selected, what is the probability that both hold at most 14 gal?

P(x ? 14) =
Mathematics
1 answer:
MariettaO [177]3 years ago
3 0

Answer:

A gasoline tank for a certain car is designed to hold 14.0 gal of gas.

\mu = 14

\sigma = 0.2

a)What is the probability that a randomly selected tank will hold at most 13.7 gal?

We are supposed to find P(x \leq 13.7)

z=\frac{x-\mu}{\sigma}

z=\frac{13.7-14}{0.2}

z=-1.5

Refer the z table for p value

p value = 0.0668

So, P(x \leq 13.7)= 0.0668

The probability that a randomly selected tank will hold at most 13.7 gal is  0.0668

b)What is the probability that a randomly selected tank will hold between 13.4 and 14.3 gal?

We are supposed to find P(13.4

z=\frac{x-\mu}{\sigma}

z=\frac{13.4-14}{0.2}

z=-3

P(x<13.4)=P(z<-3)= 0.0013

z=\frac{x-\mu}{\sigma}

z=\frac{14.3-14}{0.2}

z=1.5

P(x<14.3)= 0.9332

P(13.4

The probability that a randomly selected tank will hold between 13.4 and 14.3 gal is 0.9319

(c) If two such tanks are independently selected, what is the probability that both hold at most 14 gal?

We are supposed to find P(x \leq 14)

z=\frac{x-\mu}{\sigma}

z=\frac{14-14}{0.2}

z=0

Refer the z table for p value

p value = 0.5

So, P(x \leq 14)= 0.5

Two such tanks are independently selected, the probability that both hold at most 14 gal = 0.5 * 0.5 = 0.25

Hence If two such tanks are independently selected, the probability that both hold at most 14 gal is 0.25

You might be interested in
Hudson runs 4 miles per day. What is the relationship between the number of days and how many miles he has run
Citrus2011 [14]

Answer:

Running 3 miles a day, paired with a healthy diet and lifestyle habits, can help you burn excess body fat. ... The key to losing weight is establishing a caloric deficit, or burning more calories than you take in, and running is great for burning calories.May 28, 2019

Step-by-step explanation:

6 0
3 years ago
Patrick made a cake for his mother's birthday. He started making the
zlopas [31]

Answer: 11:15 AM

Step-by-step explanation:

9:00 plus an hour and 15 minutes (75 minutes) makes it 10:15.  Then bake for an hour (60 minutes), makes it 11:15

4 0
3 years ago
How many solutions does the system below have?<br> y=1/2x+1<br> 2y - x = 2
kvasek [131]

Answer:

infinitely many

Step-by-step explanation:

Rewrite these equations as

y = (1/2)x + 1

2y = x + 2

and then solve the second for y:  y = (1/2)x + 1.  Note that these end results are identical.  The two lines coincide; that is, one lies right on top of the other.  Thus, there  are infinitely many solutions.

3 0
3 years ago
PLEASE HELPPPPPPpppppppppppppppppppppp
Usimov [2.4K]
Its 4 by the way cause it is
6 0
3 years ago
Determining rational and irrational numbers quick 25 pts
Arlecino [84]
11/15 + 7 ⇒ rational ⇒ the sum of two rationals is always rational

√14+13 ⇒ irrational ⇒ the sum of a rational and an irrational  is always irrational

30×√6 ⇒ irrational ⇒ the product of a nonzero rational and an irrational  is always irrational

11/12 × 7/15 ⇒ rational ⇒ the product of two rationals is always rational
4 0
3 years ago
Read 2 more answers
Other questions:
  • How do you solve this 2 step equation: 8+b/-4=5
    5·1 answer
  • 60+42.95x=25+49.95x please help
    14·2 answers
  • While passing a slower car on the highway, i accelerate uniformly from 12 m/s to 24 m/s in a time of 10.0s. How far do you trave
    9·1 answer
  • Which of the following shapes has an apex? Select all that apply.
    5·2 answers
  • The following is an incomplete paragraph proving that the opposite angles of parallelogram ABCD are congruent:
    7·2 answers
  • I need help with this question will mark brainliest
    15·2 answers
  • Which of the 3 is the answer?​
    9·2 answers
  • Which expression is equivalent to 20?
    6·2 answers
  • A rectangular flower garden in Samantha's backyard has 220 feet around its edge. The width of the garden is 50 feet. What is the
    12·1 answer
  • Pls i need help guys​
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!