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sertanlavr [38]
3 years ago
12

An educational psychologist wishes to know the mean number of words a third grader can read per minute.

Mathematics
1 answer:
Rama09 [41]3 years ago
5 0

Answer: 208.

Step-by-step explanation:

The formula to find the minimum sample size is given by :-

n= (\dfrac{z^*\times \sigma}{E})^2                                    (1)

, where z* = critical z-value (two tailed).                                                                      

\sigma = Standard deviation ( from prior study ) and E = Margin of error.

As per given , we have

Margin of error : E= 0.29

Confidence level = 85%

Significance level =\alpha=1-0.85=0.15

Using z-table , the critical value (two -tailed)=z^*=z_{\alpha/2}=z_{0.15/2}=z_{0.075}=1.439

As per previous study , Variance =\sigma^2=8.41

\sigma=\sqrt{8.41}=2.9

Now, the required minimum sample size = n= (\dfrac{(1.439)\times (2.9)}{0.29})^2   [Substitute the values in formula (1)]

n=(14.39)^2

n=207.0721\approx208  [ Round to the next integer]

Hence, the minimum number of third graders that must be included in a sample = 208.

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the answer is letter C.

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2 years ago
4x^2-16=x^2+32<br> Using reverse PEMDAS
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Answer:

x = ±4 (x = 4 and x = -4)

Step-by-step explanation:

4x²-16 = x²+32

3x²-16 = 32

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5 0
2 years ago
A standard oil drum is a cylinder with a volume of approximately 218.276 liters (or 0.218276 cubic meters). The cost of producin
Arte-miy333 [17]

Answer:

r = 2,85 feet

h = 8,56 feet

Step-by-step explanation:

Area of two circular caps (m ^(2)) : 2* pi* r^(2) (where  r is the radius of circular cap)     Area of wall (m ^(2))  is 2*pi*r*h (where h is the height of drum)

V= pi*r^(2)*h           so  h=V/pi*r^(2)   (1)

Cost in $:

Cost of wall 25 $/m^(2) plus 10% for manufacturing so:

C(w) = 27,5*2*pi*r*h $/square feet

Cost of (both top and bottom cap) = 2*40,97*pi* r^(2) so:

C(caps) = 257,29* r^(2) $/squaer feet

Total cost of cylnder = cost of wall + cost of caps

Total cost f cylinder: F(c)= 55*pi*r*h+257,29* r^(2)

F(c) = 172,7*r*h + 257,29*r^(2)         F(c)  is F(r)

Since from (1) we have h=218,276/pi*r^(2)  

F(r) = (172,7)*r*(69,514)/r^(2) +257,29*r^(2)           F(c) = 12005/r + 257,29*r^(2)

Taken the first dervative

F´(r)= -12005*(1)/r^(2) +2*257,29*r         F´(r) =  -12005*(1)/r^(2) +514,58*r

f F´(r) = 0          -12005*(1)/r^(2) + 514,58*r =0

-120005 + 514,58*^(3) = 0          514,58*^(3) = 12005      r =cubic root (23,32)

r = 2,85 ft

if we replace this value en F(r) we can see F(r) tend to infinite both when r tend to 0 and when r tends to infnite so there is a minimun for the functon

r = 2,85 ft    and   h = 8,56 ft

5 0
3 years ago
Edison Research gathered exit poll results from several sources for the Wisconsin recall election of Scott Walker. They found th
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Answer: Our required probability is 0.515.

Step-by-step explanation:

Since we have given that

Probability that the respondents voted in favor of Scot Walker P(F) = 56%

Probability that the respondent voted in not favor of Scot Walker = 100-56 = P(F')=44%

Probability of those who did vote in favor had a college degree = 36% = P(C|F)

Probability of those who did vote against had a college degree = 44% = P(C|F')

So, we will use "Conditional Probability":

probability that he voted in favor of Scott Walker given that they had a college degree is given by

P(F|C)=\dfrac{0.56\times 0.36}{0.56\times 0.36+0.44\times 0.43}\\\\P(F|C)=0.515

Hence, our required probability is 0.515.

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