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podryga [215]
3 years ago
11

A random variable x x has a Normal distribution with an unknown mean and a standard deviation of 12. Suppose that we take a rand

om sample of size n = 36 n=36 and find a sample mean of ¯ x = 98 x¯=98 . What is a 95% confidence interval for the mean of x x ?
Mathematics
1 answer:
Paul [167]3 years ago
8 0

Answer:

95% Confidence Interval: (94.08,101.92)    

Step-by-step explanation:

We are given the following in the question:

Sample mean, \bar{x} = 98

Sample size, n = 36

Alpha, α = 0.05

Population standard deviation, σ = 12

95% Confidence Interval:

Formula:

\mu \pm z_{critical}\frac{\sigma}{\sqrt{n}}

Putting the values, we get,

z_{critical}\text{ at}~\alpha_{0.05} = 1.96

98 \pm 1.96(\dfrac{12}{\sqrt{36}} ) = 98 \pm 3.92 = (94.08,101.92)

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Which equation below represents a line with a slope of - 2/3 that passes through the point (-4.5 , 10)?
Lostsunrise [7]

Answer:

Option C

Step-by-step explanation:

If a line passes through a point, then that point is called a solution to the line's equation. Substituting the x and y values of that solution into the equation will give a true statement. So, to find out which option is correct, we can substitute the x and y values of (-4.5, 10) into each equation and see if the result is a true statement.  

Let's try this with option C. To make things easier, convert -4.5 into decimal form: -4\frac{1}{2}. Substitute -4\frac{1}{2} for x and 10 for y in the equation, then solve:  

y = -\frac{2}{3} x+7\\\\10 = -\frac{2}{3} (-4\frac{1}{2} )+7\\10 = -\frac{2}{3} (-\frac{9}{2})+7\\10 = 3+7\\10 = 10

10 does equal 10, so this is a true statement. Option C is the right answer.

8 0
2 years ago
a veterinarian needs to know animals weight in kilograms. if 20 pounds is about 9 kilograms and a dog weights 30 pounds, use a r
ahrayia [7]

For this case we have the following conversion:

20 pounds = 9 kilograms

To use the table what we must do is find another relationship that allows us to find the weight in kilograms for 30 pounds.

For example, half the weight in pounds is half the weight in kilograms.

Therefore, the given conversion is:

10 pounds = 4.5 kilograms

So, for 30 pounds, we multiply this last ratio obtained by three on both sides:

30 pounds = 13.5 kilograms

Then, the table is:

Pounds 10 20 30

kilograms 4.5 9 13.5

Answer:

Using the ratio table the dogs weight is:

30 pounds = 13.5 kilograms

3 0
3 years ago
Read 2 more answers
(a) For the sequence 11,13,15,17,............find the 13th term<br>​
laila [671]

Answer:

35

Step-by-step explanation:

the pattern is +2 so the answer is 35

3 0
3 years ago
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Find the midpoint of the segment with the following endpoints. (10, 7) and (5, 4)
KatRina [158]

Answer:

\frac{15}{2} , \frac{11}{2}

Step-by-step explanation:-

To find the midpoint, the equation we use is:-

\frac{x1 +x2}{2} , \frac{y1 + y2}{2}

x1 = 10

x2 = 5

y1 = 7

y2 = 4

Substituting the values in the equation, we get:-

\frac{10+5}{2} , \frac{7+4}{2}

Coordinates of the midpoint---> \frac{15}{2} , \frac{11}{2}

8 0
3 years ago
2 1/8 of 450 with solution
nika2105 [10]

Answer:

Step-by-step explanation:

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450×21/8=1181,25

5 0
3 years ago
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