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Lilit [14]
2 years ago
5

4. Amazon executives believe that at least 70% of customers would return a product 2 days after it arrives at their home. A samp

le of 500 customers found 68% returned the product they purchased prior to the third day. Given the executives' estimate, what would be the probability of a sample result with 68% or fewer returns prior to the third day
Mathematics
1 answer:
inysia [295]2 years ago
7 0

Using the <u>normal distribution and the central limit theorem</u>, it is found that there is a 0.1635 = 16.35% probability of a sample result with 68% or fewer returns prior to the third day.

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, for a proportion p in a sample of size n, the sampling distribution of sample proportions has mean \mu = p and standard error s = \sqrt{\frac{p(1 - p)}{n}}

In this problem:

  • Sample of 500 customers, hence n = 500.
  • Amazon believes that the proportion is of 70%, hence p = 0.7

The <u>mean and the standard error</u> are given by:

\mu = p = 0.7

s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.7(0.3)}{500}} = 0.0205

The probability is the <u>p-value of Z when X = 0.68</u>, hence:

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

By the Central Limit Theorem

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

Z = \frac{0.68 - 0.7}{0.0205}

Z = -0.98

Z = -0.98 has a p-value of 0.1635.

0.1635 = 16.35% probability of a sample result with 68% or fewer returns prior to the third day.

A similar problem is given at brainly.com/question/25735688

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432

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8 0
3 years ago
You have been hired as a marketing consultant to Johannesburg Burger Supply, Inc., and you wish to come up with a unit price for
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Answer:

The demabd function is:

q(p)= -4500p+18000

Step-by-step explanation:

The demand follow the linear equation q(p)=mp+b

1. When p=$2.00 and q=9000, the equation is:

9000=m(2.00)+b     (1)

2. Whe p=$4.00 and q=0, the equation is:

0=m(4.00)+b  (2)

3. Solve equation (1) for b:

9000=2m+b\\9000-2m=2m+2m+b\\9000-2m=b

4. Replace the value of b in equation (2)

0=4m+b\\0=4m+9000-2m\\0=2m+9000\\0-9000=2m+9000-9000\\-9000=2m\\\frac{-9000}{2m}=\frac{2m}{2m}\\ -4500=m

The value of m is 4500

5. Calculate b, replacing m:

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The value of b is 18000

3 0
3 years ago
Simplify the expression 5+4+2(-3)+7+(-5)
liberstina [14]
Just use pemdas
(Parenthesis, exponents, multiplication, division, addition, subtraction)
4 0
3 years ago
-2/3 x 3/5 + 5/2 - 3/5 x 1/6
chubhunter [2.5K]

Answer:

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Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Don't get this
kap26 [50]
I'll talk you through it so you can see why it's true, and then
you can set up the 2-column proof on your own:

Look at the two pointy triangles, hanging down like moth-wings
on each side of 'OC'.

-- Their long sides are equal,  OA = OB, because both of those lines
are radii of the big circle.

-- Their short sides are equal, OC = OC, because they're both the same line.

-- The angle between their long side and short side ... the two angles up at 'O',
are equal, because OC is the bisector of the whole angle there.

-- So now you have what I think you call 'SAS' ... two sides and the included angle of one triangle equal to two sides and the included angle of another triangle.
(When I was in high school geometry, this was not called 'SAS' ... the alphabet
did not extend as far as 'S' yet, and we had to call this congruence theorem
"broken arrow".)

These triangles are not congruent the way they are now, because one is
the mirror image of the other one.  But if you folded the paper along 'OC',
or if you cut one triangle out and turn it over, it would exactly lie on top of
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So their angles at 'A' and at 'B' are also equal ... those are the angles that
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5 0
3 years ago
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