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
ehidna [41]
3 years ago
13

A simple random sample from a population with a normal distribution of 99 body temperatures has xbar = 99.10°F and s = 0.64°F. C

onstruct a 99​% confidence interval estimate of the standard deviation of body temperature of all healthy humans. (show work)
_°F < σ < _°F
Mathematics
1 answer:
motikmotik3 years ago
4 0

The general formula for the margin of error is e = (zs)/√n, when the sample size is 30 or more (otherwise, we'd need to to a t-interval).

Since we're needing a 99% confidence interval, we need to know what the positive z-score associated with this two-tailed area under the normal curve is.  This can be a little tricky if you're using a standard normal table.  What you want is a two-tailed interval that has an area of .99.  What this means is that the remaining 0.01 is divided into 0.005 on each end.  This then means that, to the right of the mean (which is 0), the area is 0.005 less than the total right-half area of 0.5, or 0.495.  The total cumulative area, then, includes this plus the left half of .5, or 0.5 + 0.495 = .0995.

Then, if all we have to go on is a cumulative standard normal table, then we need to find the area closest to 0.995 and find the corresponding z-score.  This z-score is 2.58.

Now that we have the z-score, we can now plug in all the values into the formula.  

e = (2.58 · 0.66)/√102 = 0.1686.

So the 99% confidence interval will be that far above and below the mean (which is 98.8).  So the lower limit is 98.8 - 0.1686 = 98.631, and the upper limit is 98.8 + 0.1686 = 98.967.

The TI-84 method:

This is much easier, if you're allowed to use this technology.  You begin with the STAT button, and then move over to the TESTS menu.  Then select ZInterval.  We have summary stats rather than data in this problem, so we select Stats as the input.  For the standard deviation, we put 0.66, for x-bar 98.8, for n 102, and for C-level 0.99.  Then select Calculate, and it will provide the interval at the top of the screen (98.632, 98.968).  Note that the lower limit is slightly different by this method.  This is because, when doing it by hand, we had to approximate the z-score.  This created a rounding error, albeit  a small one.

You might be interested in
1. Use the graph of the rational function
Mrrafil [7]

Answer:

As x \to -3^{+}, f(x) \to -\infty

Step-by-step explanation:

Given:

From the graph, we can conclude that:

The function has vertical asymptotes at x=-3\ and\ x=2

The function has horizontal asymptote at f(x)=0

Vertical asymptotes are those values of 'x' for which the functions tends towards infinity. Horizontal asymptote is the value of the function as the 'x' value tends to infinity.

Now, as x \to -3^{+} means the right hand limit of the function at x=-3

From the graph, the right hand limit is the right side of the asymptote of the function at x = -3. The right side shows that the function is tending towards negative infinity.

Therefore, As x \to -3^{+}, f(x) \to -\infty

4 0
3 years ago
Ruby baked fried apple pies for a bake sale if each pie contains 12 apples how many total apples did reviews
Neko [114]
Doesn't say how any pies she fried
8 0
3 years ago
Read 2 more answers
What is the correlation coefficient for the data shown in the table? 0 1 4 5
SOVA2 [1]

we know that

The correlation coefficient is a number between -1 and +1 that represent the linear dependence of two variables or sets of data

Using the function CORREL in a excel tool, calculate the correlation coefficient (r)

see the attached table

the correlation coefficient for the data in the table is equal to 1

therefore

the answer is

r=1

4 0
3 years ago
Read 2 more answers
Please help me 7th grade math operations with rational numbers
Katena32 [7]
1. Stock Market:
If a stock price decreased $2 per day for four days, then the total change in value of the stock is $8. (2 x 4)
Answer: $8.

2. Evaporation:
With the given information, we can infer that if 3 inches of water in a tank decreases each week, then 15 inches of water would decrease over the course of 5 weeks. (3 x 5)
Answer: 15 inches.

3. Football:
If a football team lost 9 yards on 3 consecutive plays, then the team's total change in position is 27 yards. (9 x 3)
Answer: 27 yards.

Hope this helps! Good luck.
5 0
2 years ago
Can you help me solve 13 please 100 points
hoa [83]

Answer: A. 70

Step-by-step explanation:

95 + 90 + 85 + 80 + 70 = 420, then divide that by 5 equals 84

4 0
3 years ago
Read 2 more answers
Other questions:
  • Scanner scanned 72 photos in 8 min. If it scans photos at a constant rate. It can scan ____ photos in 23 mins
    10·1 answer
  • Solve the formula Ax+By=C for y.
    12·1 answer
  • Which of the following does not represent a function?
    11·1 answer
  • Can someone please help me??? Its urgent. 15 Points.
    10·2 answers
  • 3. Which of the following does NOT represent a
    13·1 answer
  • If Kelly's heart beats an average of 1*10^2 times per minute , about how many times does Kelly's heart beat in a year?(1 year is
    14·1 answer
  • The table shows the value of an account x years after the account was opened. Based on the exponential regression model, which i
    14·2 answers
  • Dani tracked the number of fish she caught per fishing trip and recorded the data in a frequency table. Fish caught Frequency 0
    13·1 answer
  • Solve each system by elimination.<br><br> -9x + 4y = 7<br> -2x-4y=-18
    13·2 answers
  • Nine less than one forth of a number is 6
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!