1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
max2010maxim [7]
2 years ago
11

The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books check

ed out each day. The assistant provides the following interval estimate: from 740 to 920 books per day. If the head librarian knows that the population standard deviation is 150 books checked out per day, and she asked her assistant for a 95% confidence interval, approximately how large a sample did her assistant use to determine the interval estimate
Mathematics
1 answer:
Verdich [7]2 years ago
5 0

Answer:

n=(\frac{1.960(150)}{90})^2 =10.67 \approx 11

So the answer for this case would be n=11 rounded up to the nearest integer

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

\bar X represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma =150 represent the population standard deviation

n represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

The confidence interval for this case is given by: (740, 920)

We can find the estimate for the mean and we got:

\bar X = \frac{740+920}{2} = 830

and the margin of error is given by :

ME = \frac{920-740}{2}= 90

The margin of error is given by this formula:

ME=z_{\alpha/2}\frac{s}{\sqrt{n}}    (a)

And on this case we have that ME =90 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} s}{ME})^2   (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got z_{\alpha/2}=1.960, replacing into formula (b) we got:

n=(\frac{1.960(150)}{90})^2 =10.67 \approx 11

So the answer for this case would be n=11 rounded up to the nearest integer

You might be interested in
Which equation represents the graphed function?
Novay_Z [31]

Answer: C is your answer.

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
When Emily arrived home from school, she spent 8 minutes eating a snack. Then, she spent 15 minutes playing with her dog and 32
ziro4ka [17]
Answer: 1 hour and 40 minutes

Explanation: Add all the time together and you get 100 minutes.

100 - 60 = 40

(I’m not very good at explaining it)
7 0
2 years ago
Read 2 more answers
Find the volume make it an improper fraction then a mixed number please do a step by step explanation and I will give you brainl
Andrews [41]

Answer:

8463/32=264 15/32

Step-by-step explanation:

Let's make every fraction improper first.

7 3/4=31/4

5 2/8=42/8

6 1/2=13/2

Simplify 42/8

42/8=21/4

21/4

31/4

13/2=26/4

21/14*31/4*26/4=(21*31*26)/64=16926/64=8463/32

3 0
2 years ago
C. Look for Relationships How do the processes you used for parts A and B differ? How are they the same?
olga_2 [115]

Step-by-step explanation:

Relationship is a ver beautiful friend one answer

5 0
2 years ago
(WILL MARK BRAINLIEST) Solve x^2-4x-12=0. SHOW YOUR WORK! show and DESCRIBE EACH STEP!
Natasha_Volkova [10]
<span>x^2 - 4x - 12 = 0
factors
(x - 6)(x + 2) = 0
</span>Set (x - 6) and (x + 2)<span> equal to </span><span>0</span><span> and solve for </span><span>xx</span>.<span>
x -  6 = 0; x = 6
x + 2 = 0; x = -2

answer
x = -2 or x = 6</span>
8 0
3 years ago
Read 2 more answers
Other questions:
  • Select all the equation that represent the hanger.
    13·2 answers
  • What ordered pair is 5 units to the right and 3 units up from the origin?
    10·1 answer
  • Drag and drop the tiles with the coordinate points, so they match up with an equation that they satisfy. PLEASE HELP!
    7·2 answers
  • Train travels 60 miles in 40 minutes what is the average speed
    7·2 answers
  • Jessica rented 3 movies for a total of $13.20 the movies Cost the same amount to rent what amount in dollars and cents did Jessi
    11·1 answer
  • What are partial products for 34×28
    6·1 answer
  • Please answer this correctly
    11·1 answer
  • What is the sqare root of 81 pls help​
    11·2 answers
  • The forecast calls for a 10% chance of rain on Monday. It’s _______ that it will rain on Monday.
    11·1 answer
  • 1a. Alex skateboards at a constant speed from his house to school 4 miles away. It takes him 15 minutes. What fraction represent
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!