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
kirill115 [55]
3 years ago
7

The percentage of body fat of a random sample of 36 men aged 20 to 29 found a sample mean of 14.42. Find a 95% confidence interv

al for the mean percentage body fat of all men aged 20 to 29. Assume that percentages of body fat follow a normal distribution with a standard deviation of 6.95.
Mathematics
1 answer:
Rina8888 [55]3 years ago
5 0

Answer:

14.42-1.96\frac{6.95}{\sqrt{36}}=12.150    

14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690    

So on this case the 95% confidence interval would be given by (12.150;16.690)    

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=14.42 represent the sample mean

\mu population mean (variable of interest)

\sigma=6.95 represent the population standard deviation

n=36 represent the sample size  

Solution to the problem

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

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that z_{\alpha/2}=1.96

Now we have everything in order to replace into formula (1):

14.42-1.96\frac{6.95}{\sqrt{36}}=12.150    

14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690    

So on this case the 95% confidence interval would be given by (12.150;16.690)    

You might be interested in
NEED HELP NOW 100 POINTS WILL MARK BRAINLIEST PLZ ANSWER ALL 5 PHOTOS BELOW!!!!!!
ira [324]
The answers are as follows:
1-D
2-B
3-C
4-A
8 0
3 years ago
Read 2 more answers
Find the percent change from the first value to the second 50;30
Alex787 [66]

Answer:

-40%

Step-by-step explanation:

NV = new value

OV = old value

percent change = (NV - OV)/(OV) × 100%

percent change = (30 - 50)/(50) × 100%

percent change = -20/50 × 100%

percent change = -40%

5 0
2 years ago
Show work please :: I forgot how to solve
Vesna [10]
40 pages = 80 minutes
210 pages = ? minutes
Well, take the first fact; 40 pages in 80 minutes and use it to find how many pages per minute.
40/80=1/2
1/2 pages = 1 minute
1 page = 2 minutes
210 pages = ? minutes
210*2=420
420 minutes = 7 hours
210 pages = 7 hours
Hope this helped :)
4 0
3 years ago
How much paint is needed to paint a house ? Estimate or exact
V125BC [204]

Answer:

One gallon can of paint will cover up to 400 square feet, which is enough to cover a small room like a bathroom. Two gallon cans of paint cover up to 800 square feet, which is enough to cover an average size room. This is the most common amount needed, especially when considering second coat coverage.

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
A new photocopier works 4 times as fast as an old one. When the machines work together, a university can produce all its staff m
Usimov [2.4K]

The old photocopier can make x manuals in an hour. The new photocopier can make 4x. Combined, they made 5x manuals in an hour.

In one hour they can make 1/28 of the manuals.

1/(28*5)=1/140 is the rate.

The new photocopier can make all the manuals in 4/140 or 35 hours.

The old one can make them in 140 hours.

6 0
3 years ago
Other questions:
  • You roll a six-sided die twice. What is the probability of rolling a 2 and then an odd number?​
    12·2 answers
  • Almost a billion people on the planet don't have access to clean drinking water." if there were 7.2×109 people in the world in 2
    12·2 answers
  • 20% of the children in a sports club play tennis.
    6·2 answers
  • Tonya opens a credit card in which the minimum monthly payment is 10%. Her current balance is $1,950, not including the finance
    7·2 answers
  • 15 FIFTEEN POINTS AND BRAINLIEST!!
    6·2 answers
  • Find the point on the y-axis that is equidistant from the points (-3,0) and (3,6).
    5·2 answers
  • If q = 12, what is the value of the expression 100 - 5q?
    10·2 answers
  • C + 5 = 8<br> all explanations
    9·2 answers
  • Unit 8 Correlation and Regression
    14·1 answer
  • Matt is carpeting his bedroom. The room measures 12 feet by 14 feet. If carpet costs $2.29 per square foot, then how much will M
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!