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
bagirrra123 [75]
3 years ago
6

The mean per capita consumption of milk per year is 131 liters with a variance of 841. If a sample of 132 people is randomly sel

ected, what is the probability that the sample mean would be less than 133.5 liters
Mathematics
1 answer:
Inessa [10]3 years ago
4 0

Answer:

0.8389 = 83.89% probability that the sample mean would be less than 133.5 liters.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean per capita consumption of milk per year is 131 liters with a variance of 841.

This means that \mu = 131, \sigma = \sqrt{841} = 29

Sample of 132 people

This means that n = 132, s = \frac{29}{\sqrt{132}}

What is the probability that the sample mean would be less than 133.5 liters?

This is the p-value of Z when X = 133.5. So

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

By the Central Limit Theorem

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

Z = \frac{133.5 - 131}{\frac{29}{\sqrt{132}}}

Z = 0.99

Z = 0.99 has a p-value of 0.8389

0.8389 = 83.89% probability that the sample mean would be less than 133.5 liters.

You might be interested in
Help algebra 2 please
kati45 [8]

Answer:

Step-by-step explanation:

(f*g)(x) = (-5x² + 2x + 7) (x +1)

          = x* (-5x² + 2x + 7) + 1*(-5x² + 2x + 7)

          = x*(-5x²) + x*2x + x*7 - 5x² + 2x + 7

        = -5x³ + 2x² + 7x - 5x² + 2x + 7

        = - 5x³ + <u>2x² -5x²</u>   <u>+ 7x + 2x </u>+7   {Combine like terms}

       =  -5x³ - 3x² + 9x + 7

4) (f*g)(x) = (x² + 2x + 4)(x - 2)

                = x*(x² + 2x + 4) - 2*(x² + 2x + 4)

                = x*x² + x*2x + x*4 - 2*x² - 2*2x -2* 4

                = x³ + 2x² + 4x  -2x² -4x - 8

                = x³ - 8

2) Speed=\dfrac{distance}{time}\\\\\\= \dfrac{d(h)}{t(h)}\\\\= \dfrac{2\sqrt{h}}{3\sqrt{4h}}=\dfrac{2*\sqrt{h}}{3*2\sqrt{h}}\\\\\\=\dfrac{1}{3}

1)d(h) = \sqrt{16h^{4}}=\sqrt{2*2*2*2*h*h*h*h}=2*2*h*h=4h^{2}\\\\\\t(h) = 3h^{4}-3h^{3}-5h^{2}= h^{2}(3h^{2}-3h - 5))\\\\Speed=\dfrac{4h^{2}}{h^{2}(3h^{2}-3h-5)}\\\\=\dfrac{4}{3h^{2}-3h-5}

7 0
3 years ago
Given the diagram shown below which of the following best represents the distance from the school to the library?
Amanda [17]
To answer this question, we will use the sine law which is illustrated in the attached image.

We are given that:
The distance from school to library = a
∠A = 32
∠B = 110
b = 2.2

Substitute with the givens in the relation of the sine law to get a as follows:
(sin 32) / (a) = (sin 110) / (2.2)
a = (2.2 sin 32) / (sin 110)
distance from school to library = a = 1.2406 mi

Based on the above calculations, the best choice would be:
B. 1.2 mi

4 0
3 years ago
Read 2 more answers
A skier is trying to decide whether or not to buy a season ski pass. a daily pass cost $70. a season las costs $300. the skier w
Musya8 [376]

Answer:

hi, can you please answer mine too it's just a 1 question I really need the answer because I have to pass it later at 10 pm and it's already 9:01pm I hope you can help me:(

Step-by-step explanation:

about your question I'll just put it in the comment section:)

3 0
3 years ago
The cable company is analyzing the data from two satellite television providers to determine whether their users spend more time
Kamila [148]
Probability that a Satellite Company Y watches a recorded show 
<span>= Py(recorded) </span>
<span>= 94/159 </span>
<span>= 0.59119 </span>
<span>= 59.12% </span>
<span>≈ 59% (Rounded to the nearest percent)................ANS</span>
8 0
3 years ago
Read 2 more answers
HELP WANTED!!! 10 POINT REWARD!!!
nasty-shy [4]
-5(a + 3) = -55
(a + 3)(-5) = -55
(a + 3) (-5)/-5 = -55/ (-5)
a + 3 = 11
a + 3 (-3) = 11 (-3)
a = 8

hope this helps
8 0
3 years ago
Other questions:
  • How to find the slope of y = 4x -9
    11·2 answers
  • The percents of students who travel to school by car,bus and bike are shown for a school of 825 kids
    10·1 answer
  • X^3 times x^? equals to x^17 <br><br> what’s the missing exponent?
    10·1 answer
  • If f(x) = 4x2 - 5x + 7 and g(x) = 3x2 - 2x + 8, find f(x) + g(x). A) 7x2 - 7x + 15 B) 7x4 - 7x2 + 15 C) 7x2 + 15 D) 12x4 - 8x3 +
    8·1 answer
  • How many times as much as 0.2 is 0.02?
    8·1 answer
  • Which expression finds the measure of an angle that is coterminal with a 300° angle?
    12·2 answers
  • A right rectangular prism has a height of 2 1/2 inches, a width of 3 1/2 inches, and a length of 5 1/4 inches. What is the volum
    15·1 answer
  • According to the line plot, what is the total weight of the dog toys that weighed
    8·1 answer
  • I WILL GIVE BRAINLIEST IF CORRECT
    9·2 answers
  • Rachel has a bag of marbles. She added 6 marbles to the bag but then took out 8 marbles. The bag now has 14 marbles. How many ma
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!