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
Fed [463]
3 years ago
12

Consider the population of all 1-gallon cans of dusty rose paint manufactured by a particular paint company. Suppose that a norm

al distribution with mean μ=6
ml and standard deviation σ=0.2 ml is a reasonable model for the distribution of the variable x = amount of red dye in the paint mixture. Use the normal distribution model to calculate the following probabilities. (Round all answers to four decimal places.)

(a) P(x > 6) =

(b) P(x < 6.2)=

(c) P(x ≤ 6.2) =

(d) P(5.8 < x < 6.2) =

(e) P(x > 5.7) =

(f) P(x > 5) =
Mathematics
1 answer:
Artemon [7]3 years ago
5 0

Answer:

a) 0.5.

b) 0.8413

c) 0.8413

d) 0.6826

e) 0.9332

f) 1

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 6, \sigma = 0.2

(a) P(x > 6) =

This is 1 subtracted by the pvalue of Z when X = 6. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{6-6}{0.2}

Z = 0

Z = 0 has a pvalue of 0.5.

1 - 0.5 = 0.5.

(b) P(x < 6.2)=

This is the pvalue of Z when X = 6.2. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{6.2-6}{0.2}

Z = 1

Z = 1 has a pvalue of 0.8413

(c) P(x ≤ 6.2) =

In the normal distribution, the probability of an exact value, for example, P(X = 6.2), is always zero, which means that P(x ≤ 6.2) = P(x < 6.2) = 0.8413.

(d) P(5.8 < x < 6.2) =

This is the pvalue of Z when X = 6.2 subtracted by the pvalue of Z when X  5.8.

X = 6.2

Z = \frac{X - \mu}{\sigma}

Z = \frac{6.2-6}{0.2}

Z = 1

Z = 1 has a pvalue of 0.8413

X = 5.8

Z = \frac{X - \mu}{\sigma}

Z = \frac{5.8-6}{0.2}

Z = -1

Z = -1 has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

(e) P(x > 5.7) =

This is 1 subtracted by the pvalue of Z when X = 5.7.

Z = \frac{X - \mu}{\sigma}

Z = \frac{5.8-6}{0.2}

Z = -1.5

Z = -1.5 has a pvalue of 0.0668

1 - 0.0668 = 0.9332

(f) P(x > 5) =

This is 1 subtracted by the pvalue of Z when X = 5.

Z = \frac{X - \mu}{\sigma}

Z = \frac{5-6}{0.2}

Z = -5

Z = -5 has a pvalue of 0.

1 - 0 = 1

You might be interested in
Sole the equation problem
atroni [7]
The answer is 100!!!
6 0
3 years ago
Read 2 more answers
I need help for this question
lyudmila [28]
Number8)4n+6-2n=2(n+3) 
4n+6-2n=2n+6 then collect the like terms
(4n-2n-2n=0)
0n=0

2(3b-4)=4b-11
6b-8=4b-11 collect the like terms
(6b-4b=2b)(-11+8=-3)

answer
2b=-3 then divide both sides by 2
b=-1.5
3 0
3 years ago
Write an explicit formula for <img src="https://tex.z-dn.net/?f=a_n" id="TexFormula1" title="a_n" alt="a_n" align="absmiddle" cl
Oxana [17]

Step-by-step explanation:

tn = t1  + 2t  + t3

6 0
2 years ago
How can you check the equation after you find the value for x.
qaws [65]
Plug the value of x into the equation
7 0
3 years ago
Read 2 more answers
If 30% of the 50 dimes in the roll were minted before the year 2000,then how many dimes were minted before 2000?
rewona [7]

Answer:

15 dimes

Step-by-step explanation:

50 x .30 = 15

8 0
3 years ago
Other questions:
  • Which is wider 8 mm or 5/16 in.?
    12·1 answer
  • Trigonometry Please help.
    6·1 answer
  • Find the value of the expression
    15·1 answer
  • If α and β are the zeroes of a quadratic polynomial x²+x-2 then find the value of (α/β+2) (β/α+2)
    10·1 answer
  • Determine whether the following is an example of a sampling error or a non-sampling error. 12% of all people are left handed. A
    5·1 answer
  • For every 15 students who run track, there are 7 students who play baseball. There are 112 more students who run track than play
    13·1 answer
  • Ms. Snyder is giving a 28-question test that is made up of multiple choice questions worth 2 points each and open response quest
    15·1 answer
  • Find the area of the trapezoid
    7·1 answer
  • Wolt<br>Nisha<br>IIamy<br>World ​
    5·2 answers
  • Mind lending a hand?
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!