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nevsk [136]
3 years ago
7

These data can be approximated quite well by a N(3.4, 3.1) model. Economists become alarmed when productivity decreases. Accordi

ng to the normal model what is the probability that the percent change in worker output per hour from the previous quarter is more than 0.5 standard deviations below the mean?
Mathematics
1 answer:
Ganezh [65]3 years ago
3 0

Answer:

0.6915 is the required probability.

Step-by-step explanation:

We are given the following information in the question:

N(3.4, 3.1)

Mean, μ = 3.4

Standard Deviation, σ = 3.1

Formula:

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

We have to evaluate:

P(x > \mu-0.5(\sigma)\\P(x > 3.4-0.5(3.1))\\P(x> 1.85)

Evaluation of probability:

P( x > 1.85) = P( z > \displaystyle\frac{1.85 - 3.4}{3.1}) = P(z >-0.5)

= 1 - P(z \leq -0.5)

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

P(x > 1.85) = 1 - 0.3085=0.6915 = 69.15\%

0.6915 is the probability that the percent change in worker output per hour from the previous quarter is more than 0.5 standard deviations below the mean.

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Answer:

the answer to this complicated problem is 25

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Problem page a long distance runner starts at the beginning of a trail and runs at a rate of 6 miles per hour. one hour later, a
alukav5142 [94]
The thing you have to figure out about this is the distance for each person and the time it takes for the biker to meet the runner.  The rates we are told.  The formula is distance = rate times time.  Let's do that for the runner first.  His rate is 6 so the formula so far is d = 6t.  Now let's work on the time.  If the biker left an hour later than the runner, then the runner has been running an hour more than the biker.  Therefore, the runner's time is t + 1.  Hold off on the distance part til we do for the biker what we just did for the runner.  The biker's rate is 14, and we already decided that his time is t.  His equation is d = 14t.  Now at the exact moment the biker meets the runner their distances are the same.  So if the equation for the runner is d = 6t + 6 and the equation for the biker is d = 14t and their distances are the same, by the transitive property, their rates and times are the same as well, meaning we set them equal to each other and solve for t.  6t + 6 = 14t.  6 = 8t and t = 3/4.  This means that it took 45 minutes for the biker to meet the runner.
5 0
3 years ago
A map of Rockbridge County has a scale factor of
malfutka [58]

Answer: 6 inch

Step-by-step explanation:

From the question, we are informed that a map of Rockbridge County has a scale factor of 2.5 in = 5 miles.

When the actual distance from Fairfield to Lexington is 12 miles, the distance on the map will be:

= 12/5 × 2.5

= 2.4 × 2.5

= 6 inch

6 0
3 years ago
Alvin is planning to be out of town for the day, so he asks a friend to dog-sit his 3 dogs. Each dog eats 0.5 pounds of food eve
german

Answer:

2 cans

Step-by-step explanation:

Calculate how many pounds he needs for one day:

3(0.5)=1.5 pounds for each day Alvin is gone ( 3 represents his dogs, .5 is each dog's food)

Convert into ounces:

1.5*16=24 ounces for one day

Question: If dog food is sold in 12 oz cans, how many will he need?

24/12=2 cans

Thus, he will need 2 cans

6 0
3 years ago
If neither a nor b are equal to zero, which answer most accurately describes the product of (a + bi)(a - bi)?
Scrat [10]

Answer:  the correct option is

(D) The imaginary part is zero.

Step-by-step explanation:  Given that neither a nor b are  equal to zero.

We are to select the correct statement that accurately describes the following product :

P=(a+bi)(a-bi)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

We will be using the following formula :

(x+y)(x-y)=x^2-y^2.

From product (i), we get

P\\\\=(a+bi)(a-bi)\\\\=a^2-(bi)^2\\\\=a^2-b^2i^2\\\\=a^2-b^2\times (-1)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }i^2=-1]\\\\=a^2+b^2.

So, there is no imaginary part in the given product.

Thus, the correct option is

(D) The imaginary part is zero.

3 0
3 years ago
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