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
jek_recluse [69]
3 years ago
13

Explanation A random sample of 100 observations from a normally distributed population possesses a mean equal to 83.2 and a stan

dard deviation equal to 6.4. Find a 95% confidence interval for μ.
Mathematics
1 answer:
Olenka [21]3 years ago
7 0

Answer:

The 95% confidence interval would be given by (81.933;84.467)    

Step-by-step explanation:

1) 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=83.2 represent the sample mean

\mu population mean (variable of interest)

s=6.4 represent the sample standard deviation

n=100 represent the sample size  

Confidence interval

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

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

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=100-1=99

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: "=-T.INV(0.025,99)".And we see that t_{\alpha/2}=1.98

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

83.2-1.98\frac{6.4}{\sqrt{100}}=81.933    

83.2+1.98\frac{6.4}{\sqrt{100}}=84.467

So on this case the 95% confidence interval would be given by (81.933;84.467)    

You might be interested in
The ages of three friends are consecutive integers. The sum of their ages is 45
Alborosie

45 = (x) + (x + 1) + (x + 2)

45 = 3x + 3

- 3

42 = 3x

/3

14 = x

45 = 14 + (14 + 1) + (14 + 2)

45 = 14 + 15 + 16

The ages of the 3 friends are 14, 15, and 16.

6 0
3 years ago
Read 2 more answers
HELP PLEASE<br> I WILL GIVE BRAINLIEST
Olegator [25]

Answer:

<h2>B</h2>

I hoped this helped :))

6 0
2 years ago
Read 2 more answers
Please help and thank you!
bogdanovich [222]

the answer is 13 :))
4 0
2 years ago
Read 2 more answers
Describe how to estimate the product of 396 and 71. Please :)
balu736 [363]
You can round 396 to 400 and 71 to 70. then you just multiply them and get 28,000. :))
4 0
2 years ago
What is the horizontal asymptote of j(x) =
Korvikt [17]

Answer: y=7

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Other questions:
  • What is the equation of the line shown in this graph
    15·1 answer
  • What is a markup that is more than 200%?
    6·1 answer
  • What is the mean of the data set? {32, 33, 34, 34, 36, 38, 38, 38, 40, 42}
    15·2 answers
  • Select the term that best describes the statement.
    6·2 answers
  • Solve for X answer asap thanks
    14·1 answer
  • Can anyone help me with this? giving brainliest to correct answer!
    11·1 answer
  • If y = 0.25(100 - y), then what is the value of y?
    7·2 answers
  • HELPPPPOMOGMGOGMGOGKM PLS ANSWER THIS CORRECTLY PLZZZ THIS IS FOR A VERY IMPORTANT TEST YOUWILL GET BRAINLIEST HELP
    13·2 answers
  • What is the value of x, rounded to the nearest tenth?
    14·2 answers
  • Elsa and two of her closest friends went out to dinner to celebrate Elsaś birthday. The bill for dinner totaled $74.80. If they
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!