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
Nostrana [21]
3 years ago
15

The lengths of lumber a machine cuts are normally distributed with a mean of 100 inches and a standard deviation of 0.3 inch. ​(

a) What is the probability that a randomly selected board cut by the machine has a length greater than 100.12 ​inches? ​(b) A sample of 41 boards is randomly selected. What is the probability that their mean length is greater than 100.12 ​inches?
Mathematics
1 answer:
ki77a [65]3 years ago
8 0

Answer:

a) 0.345

b) 0.005

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 100

Standard Deviation, σ = 0.3

We are given that the distribution of lengths of lumber is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

a) P(length greater than 100.12 ​inches)

P(x > 100.12)

P( x > 100.12) = P( z > \displaystyle\frac{100.12 - 100}{0.3}) = P(z > 0.4)

= 1 - P(z \leq 0.4)

Calculation the value from standard normal z table, we have,  

P(x > 100.12) = 1 - 0.655 = 0.345 = 34.5\%

b) Standard error due to sampling:

\displaystyle\frac{\sigma}{\sqrt{n}} = \frac{0.3}{\sqrt{41}} = 0.0468

P(length greater than 100.12 ​inches for the sample)

P(x > 100.12)

P( x > 100.12) = P( z > \displaystyle\frac{100.12 - 100}{0.0468}) = P(z > 2.564)

= 1 - P(z \leq 2.564)

Calculation the value from standard normal z table, we have,  

P(x > 100.12) = 1 - 0.995 = 0.005

You might be interested in
A rectangle is 9ft long and 40 in wide what is its area in square feet?
Irina-Kira [14]
The answer is 360 sqft

6 0
3 years ago
Find the output, y, when the input, x , is 7.<br> y=
Anton [14]
The answer to your question would be 6!
4 0
3 years ago
Can someone help me with this one ​
natta225 [31]

Answer:

22 would be your answer.

5 0
3 years ago
Radio signals travel at a rate of 3 x 10^8 meters per second. How many seconds would it take for a radio signal to travel from a
wel
Time = Distance / Speed   [ Already mentioned ]

Then, substitute the known values, 

t = (9.6 × 10⁶) / (3 × 10⁸)

t = 3.2 × 10⁻² s

In short, Your Answer would be Option B

Hope this helps!
4 0
3 years ago
An organisation buys a truck on hire purchase The cost is 500000 The contract states a deposit or 35% and 12 annual payments of
Mama L [17]

Answer:

total finance cost is 274064

interest in 5 year = 17568.21

creditors reduced in year 8 is 21812.87

Step-by-step explanation:

given data

cost = 500000

rate 35%

installment = 12

annual payment = 49922

to find out

the total finance cost and interest is charged in 5 year and creditors reduced in year 8

solution

we know cost is 500000 so down payment will be

payment = 35% of 500000 = 35/100 × 500000

so payment = 175000

and 12 installment purchase price is 12 ×  49922

purchase price = 599064

so total finance cost is payment + purchase price - cost

finance cost = 175000 + 599064 - 500000

so total finance cost is 274064

and

we know in 1 to 12 digit sum is 78

so interest in 5 year

interest = 5/78 of total finance cost

interest = 5/78 × 274064

interest in 5 year = 17568.21

and

interest in 8 year

interest = 8/78 of total finance cost

interest = 8/78 × 274064

interest in 8 year = 28109.13

so

creditors reduced in year 8  = 49922- 28109.13

creditors reduced in year 8 is 21812.87

4 0
3 years ago
Other questions:
  • How can you figure out <br>powers of ten
    15·1 answer
  • How many pounds of iron are produced from 4,200 pounds of iron ore if the ratio of iron ore is 5/21
    10·1 answer
  • An elephant sleeps 12% of a day what fraction of a day does an elephant sleep
    13·1 answer
  • Please help with this question?
    7·1 answer
  • Chris needs $858 to buy a computer. She has already saved $575. She gets $15 an hour for babysitting and will babysit 12 hours i
    14·1 answer
  • Select two ratios that are equivalent to 7: 10.
    13·1 answer
  • Help me please im very confused and im i wrong on my question?
    9·2 answers
  • Please help me answer this
    14·2 answers
  • Find the slope of the line graphed below.
    13·2 answers
  • ¿Cuál expresión equivale a 12 dividido entre raíz de 3
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!