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
sashaice [31]
3 years ago
8

Suppose a batch of metal shafts produced in a manufacturing company have a standard deviation of 1.5 and a mean diameter of 205

inches. If 79 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.3 inches
Mathematics
1 answer:
Crank3 years ago
6 0

Answer:

P(205-0.3=204.7

z=\frac{204.7-205}{\frac{1.5}{\sqrt{79}}}=-1.778

z=\frac{205.3-205}{\frac{1.5}{\sqrt{79}}}=1.778

So we can find this probability:

P(-1.778

And then since the interest is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.3 inches using the complement rule we got:

P = 1-0.9243 = 0.0757

Step-by-step explanation:

Let X the random variable that represent the diamters of interest for this case, and for this case we know the following info

Where \mu=205 and \sigma=1.5

We can begin finding this probability this probability

P(205-0.3=204.7

For this case they select a sample of n=79>30, so then we have enough evidence to use the central limit theorem and the distirbution for the sample mean can be approximated with:

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

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

And we can find the z scores for each limit and we got:

z=\frac{204.7-205}{\frac{1.5}{\sqrt{79}}}=-1.778

z=\frac{205.3-205}{\frac{1.5}{\sqrt{79}}}=1.778

So we can find this probability:

P(-1.778

And then since the interest is the probability that the mean diameter of the sample shafts would differ from the population mean by more than 0.3 inches using the complement rule we got:

P = 1-0.9243 = 0.0757

You might be interested in
How to do these first four please! I believe graphing quadratics thx!! Need ASAP
sergeinik [125]
Graphed it
If you need to do it manualy, consider using a table of values

5 0
3 years ago
A distance of 30 miles on a map is represented by a 2-inch line. If the map is enlarged to 3 times its size, what will be the sc
vichka [17]

Answer:

\frac{1}{5}\frac{in}{miles}

Step-by-step explanation:

we know that

The original scale of the map is

\frac{2}{30}\frac{in}{miles}=\frac{1}{15}\frac{in}{miles}

If the map is enlarged to 3 times its size

then

the new scale will be

\frac{2*3}{30}\frac{in}{miles}=\frac{6}{30}=\frac{1}{5}\frac{in}{miles}

4 0
3 years ago
the midpoint of [KL] is (-8, 1). one endpoint is K(-6, 5). find the coordinates of the other endpoint L
ExtremeBDS [4]

the correct question is

The midpoint of kl is m(–8, 1). one endpoint is k(–6, 5). find the coordinates of the other endpoint l.


we know that

the formula of midpoint is

Xm=(x1+x2)/2----> 2*Xm=x1+x2------> x2=2*Xm-x1

Ym=(y1+y2)/2----> 2*Ym=y1+y2------> y2=2*Ym-y1


let

(x1,y1)-------> (–6, 5).

(Xm,Ym)-----> (-8,1)


find (x2,y2)

x2=2*Xm-x1-----> 2*(-8)-(-6)----> -10

 y2=2*Ym-y1----> 2*(1)-5-----> -3


the point l is (-10,-3)




3 0
3 years ago
PLS SOLVE ASAP!!!<br> These points are linear.<br> Find the slope.
Lubov Fominskaja [6]
Could be y=8x + 16?
The gradient is 8 bcause each time x increases by one y increases by 8
5 0
3 years ago
Which linear function represent the table?​
rodikova [14]

Answer:

Step-by-step explanation:So, if the graph is a straight line, it is the graph of a linear function. From a table, you can verify a linear function by examining the x and y values. The rate of change for y with respect to x remains constant for a linear function. This rate of change is called the slope.Mar 9, 2011

7 0
2 years ago
Read 2 more answers
Other questions:
  • Lorenzo rides his bike at a rate of 5 yards per second. About how many miles per hour can Lorenzo ride his bike?
    11·1 answer
  • What is the range of the function f(x) = 12 - 3x for the domain {-4,-2, 0, 2, 4}?
    5·1 answer
  • What is the standard form of this number 1.46e-6
    15·2 answers
  • PLEASE HELP
    9·2 answers
  • What is 30% of 180 show work
    6·1 answer
  • Which graph represents a function
    8·1 answer
  • A video game randomly chooses your car color and type. The probability of
    7·1 answer
  • Does anyone know this answer
    5·1 answer
  • Which organism has an exoskeleton<br> crab<br> tree<br> deer<br> elephant<br> PLS HURRY!!!!
    9·2 answers
  • T and F - question with a screenshot
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!