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
Yakvenalex [24]
3 years ago
7

A standard weight known to weigh 10 grams. Some suspect bias in weights due to manufacturing process. To assess the accuracy of

a laboratory scale,that weight is weighed repeatedly. The scale readings are normally distributed with unknown mean. The population standard deviation of the scale readings is known to be 0.0003 gram.
(a) The weight is weighed FIVE times. The mean result is 10.0044 grams. Give a 98% confidence interval for the mean weight. Please keep 5 decimals in your answer.
(
,
)

(b) How many measurements must be averaged to get a margin of error of +/- 0.0001 with 98% confidence? Your answer must be a whole number.
Mathematics
1 answer:
notsponge [240]3 years ago
7 0

Answer:

a) The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams

b) 49 measurements are needed.

Step-by-step explanation:

Question a:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.98}{2} = 0.01

Now, we have to find z in the Ztable as such z has a pvalue of 1 - \alpha.

That is z with a pvalue of 1 - 0.01 = 0.99, so Z = 2.327.

Now, find the margin of error M as such

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 2.327\frac{0.0003}{\sqrt{5}} = 0.00031

The lower end of the interval is the sample mean subtracted by M. So it is 10.0044 - 0.00031 = 10.00409 grams

The upper end of the interval is the sample mean added to M. So it is 10 + 0.00031 = 10.00471 grams

The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams.

(b) How many measurements must be averaged to get a margin of error of +/- 0.0001 with 98% confidence?

We have to find n for which M = 0.0001. So

M = z\frac{\sigma}{\sqrt{n}}

0.0001 = 2.327\frac{0.0003}{\sqrt{n}}

0.0001\sqrt{n} = 2.327*0.0003

\sqrt{n} = \frac{2.327*0.0003}{0.0001}

(\sqrt{n})^2 = (\frac{2.327*0.0003}{0.0001})^2

n = 48.73

Rounding up

49 measurements are needed.

You might be interested in
On a map drawn to scale, 2cm represents 870km. How long would a line segment be that represents 130 kilometres?
Archy [21]
870/2 = 435
130/435 = 26/87 = 0.5977 cm
8 0
3 years ago
50 pointssssssss Simplify the following. Please leave it in exponential form.<br><br><br>3^8 × 1/3^1
skelet666 [1.2K]

Answer:

3^7

Step-by-step explanation:

We know that 3^8=3\cdot3^7and since it's multiplied by \frac{1}{3} which is the same thing as \frac{1}{3}^1we know that 3\cdot\frac{1}{3}\cdot3^7=3^7.

5 0
3 years ago
Read 2 more answers
Gina received a 30% discount on a new
gizmo_the_mogwai [7]

Answer:

64.94

Step-by-step explanation:

(49.95•30%)+49.95

3 0
3 years ago
Read 2 more answers
Which number is bigger? 419.10 or 419.099? please help me I do NOT want homework!
lesya [120]

Answer:

419.10 is greater than 419.099

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
How many different groups of 5 shirts can he take
professor190 [17]
2?? I’m pretty sure
Sorry if it’s wrong
3 0
3 years ago
Other questions:
  • The slope is -5/3. What is the equation for the slope?
    11·1 answer
  • Mrs. Li wants to compare her students’ test scores to the school average. She created a table to help her. Mrs. Li’s Student Tes
    14·3 answers
  • Find all angle measures in the diagram.
    14·1 answer
  • Need Help Fast!!! 10 points!
    7·1 answer
  • A selection of staff wages is collected and shown below. £254 £254 £310 £276 £116 £90 £312 £180 £180 £536 £350 £243 £221 £165 £2
    7·2 answers
  • Hi! if anyone can help me, it would be very nice :D
    12·1 answer
  • The volume of the large cube is 125 cubic inches. The volume of the small cube is 27 inches. What is the difference between the
    11·1 answer
  • Please answers asap i will give brainmaster
    8·1 answer
  • PLS HELP ILL MARK U BRAINLIEST<br> I DID THE FIRST 1 I NEED HELP WITH THE SECOND &lt;3
    6·1 answer
  • Find the mean of the first five whole numbers​
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!