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]
2 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:
motikmotik2 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
Which equation represents the data shown in the table below
Debora [2.8K]
It is obviously C.  most obviously
8 0
2 years ago
Read 2 more answers
What is the y-intercept of this equation?<br> y= 2/9x +13
Ksju [112]

Answer:

13

Step-by-step explanation:

y=mx+b

b= y-intercept

5 0
3 years ago
Read 2 more answers
Unit 2 Functions Classwork - Homework Day 5 Piecewise Functions
trasher [3.6K]
Yatrsiwnbcshsutacshbsvsy
6 0
3 years ago
a recipe for lasagna calls for 3 pounds of tomatoes to serve 5 people. a caterer wants to make enough lasagna to serve 110 peopl
Roman55 [17]
To do this you want to divide 110 by 5 to get 22.  Now you want to multiply 3 by 22. That means the caterer need 66 pounds of tomatoes.
5 0
3 years ago
Which expression can be used to check the answer to 56 ÷ (-14) = n?
kozerog [31]
A. Multiplication is the ONLY function that reverses what division did. If you did 56/-14 = n, then n x -14 should equal 56.
6 0
2 years ago
Read 2 more answers
Other questions:
  • A plumber has a 2.5 meter long copper pipe. He needs to cut lengths of 60cm,35cm and 90cm
    12·1 answer
  • Lo
    14·1 answer
  • 10 cards are numbered from 1 to 10 and placed in a box. One card is selected at random and is not replaced. Another card is then
    14·1 answer
  • In converting 9 inches to yards, what unit (omit the number) would you place
    7·1 answer
  • Ethan says that the value of 40.7 is 10 times the value of 4.07 is be correct?
    15·1 answer
  • Suppose that two teams are playing a series of games, each of which is independently won by team A with probability p and by tea
    14·1 answer
  • In the real world describe 2 objects that are similar
    12·2 answers
  • Solve for x in the figure below
    11·2 answers
  • Please help it's greatly apprecatied
    14·1 answer
  • Help ..................
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!