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
OlgaM077 [116]
3 years ago
10

hompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 125 millimeters,

and a variance of 49. If a random sample of 41 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by greater than 2.2 millimeters? Round your answer to four decimal places.
Mathematics
1 answer:
choli [55]3 years ago
7 0

Answer:

P(-2.012

So since we want the probability that "the sample mean would differ from the population mean by greater than 2.2 millimeters". Then we use the complement rule and we got

P=1-0.9558=0.0442

Step-by-step explanation:

Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Let X the random variable that represent the  diameter of a population, and for this case we know the distribution for X is given by:

X \sim N(125,49)  

Where \mu=125 and \sigma=7

And let \bar X represent the sample mean, the distribution for the sample mean is given by:

\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})

On this case  \bar X \sim N(125,\frac{7}{\sqrt{41}}=1.093)

Solution to the problem

We can begin the problem finding this probability

P(\mu -2.2

We can use the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}

If we apply this formula to our probability we got this:

P(125-2.2

=P(\frac{122.8-125}{\frac{7}{\sqrt{41}}}

And we can find this probability on this way:

P(-2.012

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

P(-2.012

So since we want the probability that "the sample mean would differ from the population mean by greater than 2.2 millimeters". Then we use the complement rule and we got:

P=1-0.9558=0.0442

You might be interested in
The mean temperature for the first 4 days in January was 8°C. The mean temperature for the first 5 days in January was 7°C. What
mote1985 [20]

Answer:

The temperature of the 5th day was 3°C

Step-by-step explanation:

Mean temperature of the first 4 days = 8°C

Note that:

Mean = Sum of temperatures ÷ number of days

∴ 8 = sum of temperature ÷ 4

= 8 = \frac{sum\ of\ temperatures}{4}

= sum\ of\ temperatures\ = 8\ \times\ 4 = 32

Therefore the sum of the first 4 days = 32

Let the temperature of the next day (the fifth day) be m

Hence,

sum of the temperatures of first 5 days = 32 + m - - - - (1)

Next, the sum of the first 5 days can be calculated from the given average of the first 5 days as follows:

Mean temperature of the first 5 days = 7

Mean = \frac{sum\ of\ temperatures}{number \ of\ days}\\\\7 = \frac{sum\ of\ temperatures}{5} \\sum\ of\ temperatures\ = \ 7\ \times\ 5\ = 35\\sum\ of\ temperature\ of\ the\ first\ 5\ days\ =\ 35 - - - - - (2)

Now, you will notice that equation (1) = equation (2)

∴ 32 + m = 35

m = 35 - 32 = 3

therefore, the temperature of the 5th day was 3°C

4 0
3 years ago
A number has 2 tens and 15 ones. Write the number in words
Verizon [17]
Thirty Five all you need to do is add 20 to 15
8 0
3 years ago
Read 2 more answers
If f(x) = x2 − 6x + 3 x − 1 , what is f(−1)? A) −5 B) −2 C) 2 D) 5
ale4655 [162]

Answer:

f(-1)=3

Step-by-step explanation:

f(x)=x^2-6x+3x-1

f(x)=x^2-3x-1

f(-1)=(-1)^2-3(-1)-1

f(-1)=1+3-1

f(-1)=4-1

f(-1)=3

8 0
3 years ago
Can a radical ever be rational? Glve examples. Justify your answer using complete sentences.
pochemuha

Answer:

Yes

Step-by-step explanation:

Yes, a radical can be a rational, this is because a radical indicates the square root of a number. An example of this is \sqrt{25} = 5.

4 0
3 years ago
Read 2 more answers
What is 6.30 rounded to the nearest tenth?
Lady_Fox [76]
It's rounded to 6.3
:)
3 0
3 years ago
Read 2 more answers
Other questions:
  • 0.08×6 what is the product
    15·1 answer
  • Answer please!!!!!!!!!!!!!!!!!!!!!!
    11·1 answer
  • What is the rate of change to 2y=14x+6
    6·1 answer
  • PLEASEEEEE HELPPPP ASPPPPPPP
    6·1 answer
  • Please help and thank u
    14·1 answer
  • Diego is playing basketball. While running at 7 km/h toward a basketball hoop, he throws the ball at the net. The ball travels a
    9·2 answers
  • Complete the equation for the horizontal line that passes through (5 -7)
    15·1 answer
  • What is 18/5 as a terminating decimal (use long division)
    6·1 answer
  • That's it can you did it?​
    9·2 answers
  • Simplify the expression <br> 6m^2n-14mn^2-mn^2+2m^2n
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!