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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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Marina CMI [18]

Answer:

1.) 15

2.) -21

3.) -15

4.) 21

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
[Calculus, Derivatives] Can a function be differentiable at certain points even if the entire function is not differentiable?
koban [17]

A function is differentiable if you can find the derivative at every point in its domain. In the case of f(x) = |x+2|, the function wouldn't be considered differentiable unless you specified a certain sub-interval such as (5,9) that doesn't include x = -2. Without clarifying the interval, the entire function overall is not differentiable even if there's only one point at issue here (because again we look at the entire domain). Though to be fair, you could easily say "the function f(x) = |x+2| is differentiable everywhere but x = -2" and would be correct. So it just depends on your wording really.

5 0
4 years ago
An elevator is rated to safely hold ten 250 lb people. The elevator is loaded as follows: three 600 lbs cartons of books, Jim (1
iris [78.8K]
To do this, we will need to find how much the elevator can hold in all. Multiply 10 by 250 to get 2500. Since it can also hold 10% more, multiply 2500 and 0.10 to find out how much 10% is. You get 250. Add 2500 and 250 to get how much the elevator can safely hold. It would be 2750.

To find out how much more weight can be added, first find out how much weight is on the elevator collectively. (books) 600+ (Jim) 180+ (Gavin) 330 + (Deb) 250 + (Susan) 120 = 1480. Subtract this from the amount the elevator can hold, and you get how much more weight can be added. 2750-1480= 1270.

The elevator can hold 1270 more ibs.
6 0
3 years ago
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A plane leaves at 11:22 am .and arrived at 3:13 pm. how long was the flight?
ale4655 [162]

Answer:

3 hours and 51 minutes

Step-by-step explanation:

Take the ending time and subtract the start time

3:13pm - 11:22am

Remember that pm means aft 12 o'clock in the after noon so add 12 hours

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15:13 - 11:22

We are subtracting more minutes than we have so we have to borrow from the hours

1 hour = 60 minutes

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7 0
3 years ago
7/8 teaspoons is 1/4 groups of what size
madreJ [45]
T × 1/4  which equals 7/8

T = 7/8 × 4  which equals  7/2


7/2 is your answer
4 0
3 years ago
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