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
Radda [10]
2 years ago
8

A catering company provides packages for weddings and for showers. The cost per person for small groups

Mathematics
1 answer:
Tomtit [17]2 years ago
5 0

Using the <em>normal distribution and the central limit theorem</em>, it is found that the probability the mean cost of the weddings is more than the mean cost of the showers is of 0.9665.

<h3>Normal Probability Distribution</h3>

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

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

  • It 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, which is the percentile of X.
  • By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation s = \frac{\sigma}{\sqrt{n}}.
  • When two variables are subtracted, the mean is the subtraction of the means, while the standard error is the square root of the sum of the variances.

<h3>What is the mean and the standard error of the distribution of differences?</h3>

For each sample, they are given by:

\mu_W = 82.3, s_W = \frac{18.2}{\sqrt{9}} = 6.0667

\mu_S = 65, s_S = \frac{17.73}{\sqrt{6}} = 7.2382

For the distribution of differences, we have that:

\mu = \mu_W - \mu_S = 82.3 - 65 = 17.3

s = \sqrt{s_W^2 + s_S^2} = \sqrt{6.0667^2 + 7.2382^2} = 9.4444

The probability the mean cost of the weddings is more than the mean cost of the showers is P(X > 0), that is, <u>one subtracted by the p-value of Z when X = 0</u>, hence:

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

By the Central Limit Theorem

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

Z = \frac{0 - 17.3}{9.4444}

Z = -1.83

Z = -1.83 has a p-value of 0.0335.

1 - 0.0335 = 0.9665.

More can be learned about the <em>normal distribution and the central limit theorem</em> at brainly.com/question/24663213

You might be interested in
Which relationship describes angles 1 and 2?
creativ13 [48]

supplementary angels as their sum = 180

4 0
3 years ago
What is the meaning of horizontal?
zepelin [54]
Going across like a horizon
4 0
3 years ago
Read 2 more answers
The equation |2x – 12|= 10 has two solutions.<br> The sum of those two solutions is
zlopas [31]

Answer:

-5 and +5

Step-by-step explanation:

add twelve to both sides

New equations: 2x= -+10

Divide by 2 on both sides

x=-5, +5

3 0
3 years ago
Read 2 more answers
What expression represents the perimeter of the rectangle?<br> shown below
Komok [63]

Answer:

4x + 4

Step-by-step explanation:

perimeter= breadth + length + breadth + length

(x+2)+(x+2)+x+x

= 4x(because there is 4 x) + 2 +2

= 4x + 4

5 0
3 years ago
What is a isometric dot paper
Nady [450]
Isometric graph paper is a triangular graph paper which uses a series of three guidelines forming a 60° grid of small triangles. The triangles are arranged in groups of six to make hexagons.
5 0
3 years ago
Read 2 more answers
Other questions:
  • Write the slope-intercept form of the equation of the line through the given points. (0,3) and (-4 -1)
    5·1 answer
  • Asia has $15.45 to buy chips for a party. Each bag costs $2.13. How many can she buy?
    7·2 answers
  • GFC if 56 and 84 . The GCF OF 84 and 56 is?
    11·2 answers
  • Find the sum of the given vectors and illustrate geometrically. [-2,-1],[5,7]
    11·1 answer
  • Please help within 30ish minutes I’m be g g in g you
    5·1 answer
  • Find a linear inequality with the following solution set. Each grid line represents one unit.
    5·1 answer
  • The Venn diagram below is used for showing odd numbers and prime numbers.
    6·1 answer
  • How do you plot x=y on a graph
    12·2 answers
  • Need help with thiss guys!!!
    12·1 answer
  • SOMEONE PLS HELP :(( thank u if u do :)))
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!