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Alina [70]
2 years ago
15

a. Show the sampling distribution of p, the proportion of groceries thrown out by your sample respondents.b. What is the probabi

lity that your survey will provide a sample proportion within 6.03 of the population proportion
Mathematics
1 answer:
Anika [276]2 years ago
7 0

Answer:

The corresponding p - value will be  is < 0.00001 which is less than 0.05

Step-by-step explanation:

Suppose p= 0.12 and n= 540 then the standard deviation can be taken out as √p(1-p)/n= √0.12(1-0.12)/540= 0.014

For the probability that the survey will provide a sample proportion within 6.03 of the population proportion

we will find the z statistic

z= p^-p/√p(1-p)/n

But √p(1-p)/n= 0.014 and p^-p= 6.03

Putting the values

z= 6.03/0.014= 430.71

The corresponding p - value will be  is < 0.00001 which is less than 0.05

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Solve this arithmetic Progression​
GREYUIT [131]

So, here in part a), we are given n terms (no specific no. of terms given), so no. of terms = n , also, the common difference is defined as the difference between the next term to a specific term and the term, i.e {\bf{d=a_{n}-a_{n-1}}}, where d is the common difference, so here d = 49 - 45 = 4

Also, here the last term is 49 let say it the nth term, as no number of terms are given, so using the Arithmetic Progression formula, we can write as ;

{:\implies \quad \sf a+(n-1)d=49}

{:\implies \quad \sf a+(n-1)4=49}

{:\implies \quad \sf a+4n-4=49}

{:\implies \quad \sf a=49+4-4n=\boxed{\bf{53-4n}}}

Now, as we assumed there are n terms, so using the sum formula, we can have ;

{:\implies \quad \sf S_{n}=\dfrac{n}{2}(a+a_{n})}

{:\implies \quad \sf S_{n}=\dfrac{n}{2}(53-4n+49)}

{:\implies \quad \sf S_{n}=\dfrac{n}{2}(102-4n)}

{:\implies \quad \sf S_{n}=n(56-2n)=\boxed{\bf{-2n^{2}+56n}}}

Now, for part b) we are given a geometric progression with first term = a = 1, common ratio = r = (3/1) = 3, and no. of terms = n = 6, so now putting all values in the sum formula we will have;

{:\implies \quad \sf S_{6}=\dfrac{1\{1-(3)^{6}\}}{1-3}}

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bv = boat velocity in still water
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bv -cv = 36
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2*bv = 90

boat velocity in still water = 45 mph

since bv + cv = 54
then we know the current velocity = 9 mph


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