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Yakvenalex [24]
3 years ago
15

Joe heard from a reliable source that only 22% of people actually sleep 8 hours or more per night. You do a survey and find 58 o

ut of 148 sleep for 8 hours or longer. Build a 95% confidence interval. Round to the nearest hundredth.
Mathematics
1 answer:
Juliette [100K]3 years ago
8 0

Answer:

95% Confidence interval:  (31.32%,47.04%)

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 148

Number of people who sleep for 8 hours or longer, x = 58

\hat{p} = \dfrac{x}{n} = \dfrac{58}{148} = 0.3918

95% Confidence interval:

\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

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

Putting the values, we get:

0.3918\pm 1.96(\sqrt{\dfrac{0.3918(1-0.3918)}{148}})\\\\ = 0.3918\pm 0.0786\\\\=(0.3132,0.4704)=(31.32\%,47.04\%)

(31.32%,47.04%)  is the required 95% confidence interval.

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Probability of green die being even: 3/6, which simplifies to 1/2 (2, 4, 6 are even and 1, 3, 5 are odd)

Probability of blue die being even: 3/6, which simplifies to 1/2.

Compound probability:
1/2* 1/2= 1/4

Final answer: 1/4
6 0
4 years ago
There are 64 pretzels in a 16 ounce bag of chocolate covered pretzels.
FromTheMoon [43]
16:64
5:x (Cross Multiply)
16x = 64*5
16x = 320 (Then Divide both sides by 16 to isolate x)
x= 20
5 0
3 years ago
For the line segment whose endpoints are X(1, 2) and Y(6, 7), find the x value for the
finlep [7]

Answer:

3) 2.7

Step-by-step explanation:

The distance between two points (x_1,y_1) and (x_2,y_2) can be determined by:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Since the points are X(1, 2) and Y(6, 7). The distance between the two points is

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(6-1)^2+(7-2)^2}=\sqrt{50}

the x value for the  point located 1/3 the distance from X to Y,

x=\frac{x_2-x_1}{3}=\frac{6-1}{3}=1.7

The x value = x_1+1.7 = 1+1.7 = 2.7

6 0
3 years ago
Read 2 more answers
19 is greater than the sum the number n and 3
masha68 [24]
Your answer should be 19>n+3
5 0
2 years ago
What is the equation of the line that passes through (2, -7) and (-1, 2)?
SVETLANKA909090 [29]

Answer:

y = -3x - 1

Step-by-step explanation:

The slope intercept form of the equation of a line is:

y = mx + b

where m is the slope, and b is the y-intercept.

First, we find the slope of the line using the two given points.

m = slope = (y2 - y1)/(x2 - x1) = (2 - (-7))/(-1 - 2) = (2 + 7)/(-3) = 9/(-3) = -3

Now we plug in the slope we found into the equation above.

y = -3x + b

We need to find the value of b, the y-intercept. We use the coordinates of one of the given points for x and y, and we solve for b. Let's use point (2, -7), so x = 2, and y = -7.

y = -3x + b

-7 = -3(2) + b

-7 = -6 + b

Add 6 to both sides.

-1 = b

Now we plug in -1 for b.

y = -3x - 1

4 0
3 years ago
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