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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.

You might be interested in
A toy manufacturer makes lightweight balls for indoor play. The large basketball uses 4 ounces of foam and 20 minutes of labor a
trapecia [35]

Answer:

(24, 224 ) i.e. 24 basketball and 224 footballs

Step-by-step explanation:

<em>Basketball :</em>

uses 4 ounces of foam

20 minutes of labor

profit = $2.50

<em>Football :</em>

uses 3 ounces of foam

30 minutes of labor

profit = $2

Manufacturer has :

768 ounces of foam , 120 labor hours per week,

<u>using the simplex method to determine the optimal production schedule so as to maximize profits </u>

lets assume

x = number of basketball

y = number of footballs

maximize = 2.5 x + 2y  from a linear programming problem

attached below is the detailed solution

6 0
3 years ago
Derick solves the problem below.
Gala2k [10]

As it is proved that the equation has no solution, Derick is correct

Step-by-step explanation:

Given

-3(4n + 2) = -4n + -2 (4n - 6)

We have to solve the equation in order to check if Derick was solved the equation correctly or not.

So,

Applying distributive property first

-12n -6 = -4n -8n +12\\-12n-6 = -12n+12\\-12n+12n-6 = 12\\-6 = 12

As the variable is already cancelled in the equation there is no unique solution.

In order for an equation to have infinite solutions the constant on both sides of equation should be same which is not the case in the given equation

So,

As it is proved that the equation has no solution, Derick is correct

Keywords: Linear equations, variables

Learn more about linear equations at:

  • brainly.com/question/5510873
  • brainly.com/question/5527192

#LearnwithBrainly

3 0
3 years ago
there are five bells which ring at interval of 4,5,12 and 15 minutes respectively at what minute those bells ring at the same ti
Rus_ich [418]
<h3>Answer:   60 minutes</h3>

=====================================================

Explanation:

Let's find the LCM of 4 and 5, which are the first two items of the list.

  • multiples of 4 are: 4,8,12,16,20,24,...
  • multiples of 5 are: 5,10,15,20,25,...

The smallest item in each list is 20, so the LCM of 4 and 5 is 20.

We can replace the "4,5" in the list "4,5,12,15" with "20". So our new list would be "20,12,15".

We then repeat the process of finding the LCM of the first two items

  • multiples of 20 are: 20,40,60,80,...
  • multiples of 12 are: 12,24,36,48,60,72,...

LCM of 20 and 12 is 60.

The list "20,12,15" condenses to "60,15".

Repeat this process of finding the LCM once more and you'll find the overall LCM is 60.

Therefore, the LCM of the entire set {4,5,12,15} is 60. This is the smallest multiple shared by all four values. Interestingly enough, the outer values pair up to multiply to 60, and so do the inner values.

4*15 = 60

5*12 = 60

The bells ring together every <u>60 minutes</u>

In other words, all of the bells ring together at the same time every hour (perhaps at the top of every hour; eg at 7:00 pm and at 8:00 pm, etc).

8 0
2 years ago
Tom starts lawn mowing business before he can begin he purchases a new lawnmower each weekend he mows the same number of lawns a
Anastasy [175]
To be able to give the answer to this item, we are to represent first with any variables the amount he earns each weekend for mowing the same field. Also, we represent the number of weeks he had worked by the variable y. The total amount of money he will have after working for y weeks is,
 
                           T = xy

Since, we are not given with any other information of the other expenses that have to be paid  then we can say that if T is already equal to the price of the new lawnmower then, Tom will be able to purchase it and begin his lawn mowing business in due time. 
7 0
3 years ago
Is 5/8 grater than or equal to 11/16
dezoksy [38]

Answer:

Less than

Step-by-step explanation:

Although it wasn't an option, it is less than. In order to accurately compare then, you have to get the least common denominator. Using the least common multiple (2), you multiply 5/8 by 2 and end up with 10/16. Now 10 is less than 11, so the option is neither of those. 5/8 is less than 11/16.

7 0
3 years ago
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