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
The sum of five consecutive numbers is -75. Which number is the least of these five numbers?
Ivan
Hello! I can help you with this! Do -75/5 to get -15. -15 will be your middle number. So for consecutive integers, -13 + -14 + -15 + -16 + -17 = 75. Those are five consecutive integers that have a sum of 75. The lowest of 5 integers is -17, because it’s the smallest of them all and the furthest to the left of the number line. A line further to the left of the number line means it’s smaller. Therefore, the rest of the five integers is -17.
6 0
3 years ago
Read 2 more answers
Determine the volume of the shaded region.
vovangra [49]
The volume of the shaded region is 1650 cubic feet.

5 0
3 years ago
in a marathon race (42.195 km), the winner’s time is 2 hours, 13 minutes, and 9 seconds, while the second-place time is 2 hours,
algol [13]

in a marathon race (42.195 km), the winner’s time is 2 hours, 13 minutes, and 9 seconds, while the second-place time is 2 hours, 26 minutes, and 6 seconds . The distance is 2.664 km.

D = distance of marathon = 42.195 km = 42195 m

tw = time taken by winner = 2 h 17 min = 2 (60) + 17 = 137 min = 137 (60) = 8220 sec

Vw = speed of winner

speed of winner is given as

Vw = D /tw = 42195/8220

ts = time taken by second place = 2 h 26 min 14 sec = 2 (60)(60) + (26)(60) + 14 = 8774 s

Vs = speed of second place

speed of second place is given as

Vs = D /ts = 42195/8774

distance of the second place holder from the finish line is given as

D' = Vs (ts - tw)

D' = (42195/8774 )(8774 - 8220)

D' = 2664.24 m

D'= 2.664 km

To learn more about distance  visit:brainly.com/question/15172156

#SPJ4

7 0
1 year ago
Find the first, fourth, and tenth terms of the arithmetic sequence described by the given rule.
lina2011 [118]

Answer is in the photo. I can only upload it to a file hosting service. link below!

tinyurl.com/wpazsebu

7 0
2 years ago
Read 2 more answers
What is the decimal 6.9 as a fraction
Verizon [17]

6.9 = 6.9 / 1

Numerator  = 6.9 × 10 = 69
Denominator  = 1 × 10 = 10

Numerator / Denominator = 69 / 10

Simplifying our fraction

= 69/10

= 69/10

= 6  9/10
5 0
3 years ago
Read 2 more answers
Other questions:
  • Annabelle traded $2250 for euros, immediately changed her mind, and then promptly traded her euros back into dollars. Which of t
    6·2 answers
  • I need help with these problems please
    14·1 answer
  • What are the types of transformations in 8th grade Pre-Algebra?
    7·1 answer
  • To make 2 batches of nut bars, Jayda needs to use 4 eggs. How many eggs are used in each batch
    14·2 answers
  • Steve cycled 35 miles in 2 1/2 hours. What was the average speed that steve travled
    6·2 answers
  • Tony’s tattoo parlor sold 389 tattoos this month. 43 of those tattoos where arm tattoos. What is the reasonable estimate of the
    11·2 answers
  • How do you turn 3 6/20 into a decimal
    5·2 answers
  • Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    11·1 answer
  • b) 7 of these cuboids of side 3 cm are put together to make this shape. Find the surface area of this shape. (3) Total marks: 5
    13·1 answer
  • The temperature is 40 below zero and remained that low for 8 days. What is the answer: a) 8, b) -8, c) 0, d) -40
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!