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
Tema [17]
3 years ago
7

A nurse is investigating the birth weights of​ non-premature babies. She selects a random sample of 41 such​ babies, and found a

mean weight of 3506.4 grams and a sample standard deviation of
494.2 grams. Find a 95​% confidence interval for the mean birth weight of all ​non-premature babies. Show your calculation for the confidence interval as well as the final confidence interval rounded to one decimal place. Then write a sentence that gives the interpretation of your confidence​ interval, including the correct units.
Mathematics
1 answer:
kherson [118]3 years ago
6 0

Answer:

The 95​% confidence interval for the mean birth weight of all ​non-premature babies is between 3350.4 grams and 3662.4 grams. This means that we are 95% sure that true mean birth weight of all non-premature babies is in this interval.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 41 - 1 = 40

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 40 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.95}{2} = 0.975. So we have T = 2.0211

The margin of error is:

M = T\frac{s}{\sqrt{n}} = 2.0211\frac{494.2}{\sqrt{41}} = 156

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 3506.4 - 156 = 3350.4 grams

The upper end of the interval is the sample mean added to M. So it is 3506.4 + 156 = 3662.4 grams

The 95​% confidence interval for the mean birth weight of all ​non-premature babies is between 3350.4 grams and 3662.4 grams. This means that we are 95% sure that true mean birth weight of all non-premature babies is in this interval.

You might be interested in
WILL GIVE BRAINLIEST
Elza [17]

Answer:

99 people is the answer

Step-by-step explanation:

.48 x 208 = 99

7 0
3 years ago
Read 2 more answers
Need help + Fast! I suck at math
liberstina [14]
Your answer is C: c = 2.50 + 2.50n

To get this answer I looked at the possible answers and inserted the numbers from the chart to see which fit.
3 0
3 years ago
jack buys a pool with 400 gallons , and it take 8 hours to fill. How many gallons were poured per hour?​
IrinaK [193]

Answer:

50 gallons per hour

Step-by-step explanation:

400/8 = 50

4 0
3 years ago
Read 2 more answers
On 1st January 2020, Laurie invests P dollars in an account that pays a nominal annual interest rate of 5.5%, compounded quarter
andrezito [222]

Answer:

1) The common ratio =  1.055

2) The year in which the amount of money in Laurie's account will become double is the year 2032

Step-by-step explanation:

1) The given information are;

The date Laurie made the investment = 1st, January, 2020

The annual interest rate of the investment = 5.5%

Type of interest rate = Compound interest

Therefore, we have;

The value, amount, of the investment after a given number of year, given as follows;

Amount in her account = a, a × (1 + i), a × (1 + i)², a × (1 + i)³, a × (1 + i)ⁿ

Which is in the form of the sum of a geometric progression, Sₙ given as follows;

Sₙ = a + a × r + a × r² + a × r³ + ... + a × rⁿ

Where;

n = The number of years

Therefore, the common ratio = 1 + i = r = 1 + 0.055 = 1.055

The common ratio =  1.055

2) When the money doubles, we have;

2·a = a × rⁿ = a × 1.055ⁿ

2·a = a × 1.055ⁿ

2·a/a = 2 = 1.055ⁿ

2 = 1.055ⁿ

Taking log of both sides gives;

㏒2 = ㏒(1.055ⁿ) = n × ㏒(1.055)

㏒2 = n × ㏒(1.055)

n = ㏒2/(㏒(1.055)) ≈ 12.95

The number of years it will take for the amount of money in Laurie's account to double = n = 12.95 years

Therefore, the year in which the amount of money in Laurie's account will become double = 2020 + 12..95 = 2032.95 which is the year 2032

The year in which the amount of money in Laurie's account will become double = year 2032.

3 0
3 years ago
What is |3| - 7...............
Ad libitum [116K]
The absolute value of 3 =3
So 3-7= -4
6 0
3 years ago
Other questions:
  • Based on the Fundamental Theorem of Algebra, how many complex roots does each of the following equations have? Write your answer
    7·2 answers
  • Given h(x) = -x + 1, find h(0)
    7·2 answers
  • Its coordinate plane plz help
    14·1 answer
  • Which of the following expressions is in simplified form?
    6·2 answers
  • (08.04 MC)
    12·1 answer
  • Please please help so I can finish this
    14·1 answer
  • A bag contains pennies, nickles, dimes, and quarters.There are 50 coins in all. Of the coins, 10% are pennies and 32% are dimes.
    14·1 answer
  • Fresh Fruits sells 10 lemons for $2.50. What is the price for 1 lemon
    14·2 answers
  • Find the length of the hypotenuse
    8·1 answer
  • Write an equation and explain what the variables represent, please help.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!