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vladimir1956 [14]
3 years ago
8

A statistics instructor designed an exam so that the grades would be roughly normally distributed with a mean of and a standard

deviation of 1015. In the space provided, draw a sketch of this distribution and label the mean and, using the standard deviation, two additional points on the horizontal axis. (2 pts)

Mathematics
1 answer:
WARRIOR [948]3 years ago
4 0

Answer:

a) Figure attached

b) P(X\geq 90)=P(\frac{X-\mu}{\sigma}\geq \frac{90-\mu}{\sigma})=P(Z \geq\frac{90-75}{10})=P(z>1.5)

And we can find this probability with the normal standard table and with the complement rule:

P(z\geq 1.5)=1-P(z

Step-by-step explanation:

A statistics instructor designed an exam so that the grades would be roughly normally distributed with a mean of μ=75 and a standard deviation of σ= 10.

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".  

Part a

Figure attached.

Part b

What proportion of students are expected to earn grades of ≥90?

We are interested on this probability

P(X\ geq 90)

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

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

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

P(X\geq 90)=P(\frac{X-\mu}{\sigma}\geq \frac{90-\mu}{\sigma})=P(Z \geq\frac{90-75}{10})=P(z>1.5)

And we can find this probability with the normal standard table and with the complement rule:

P(z\geq 1.5)=1-P(z

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den301095 [7]

Using proportions, it is found that the life span of the person would be 14 years, 212 days and 22 hours shorter.

---------------------------

  • 2 packs a day for 35 years is 40 cigarettes a day for 12775 days, as 35 \times 365 = 12775.
  • Thus, a total of 511000 cigarettes, as 40 \times 12775 = 511000.
  • Assuming each cigarette costs 15 minutes of life, the person loses 7665000 minutes of life, as 15 \times 511000 = 7665000

  • One year has 525600 minutes, thus the person loses 14 years of life, as \frac{7665000}{525600} = 14.5833333
  • Looking at the decimal part, the person loses 212 days of life, as 0.5833333 \times 365 = 212.916666655
  • Again looking at the decimal part, 22 hours, as 0.916666655 \times 24 = 22

  • Thus, the person loses 14 years, 212 days and 22 hours of life.

A similar problem is given at brainly.com/question/23352001

6 0
2 years ago
Expand 2(p+q) ??????
soldier1979 [14.2K]

Answer:

2p+2q

Step-by-step explanation:

7 0
3 years ago
PLEASE HELP ME ASAP
velikii [3]

Answer:

Radius r=0.30m, Velocity, v=36m/s

(a) angular speed w=

r

v

=

0.3

36

=120rad/s

(b) final angular speed w

′

=0

From rotational kinematics w

′

2

−w

2

=2αθ

0−14400=2α×40×2π

⇒α=

160π

−14400

=−28.6rad/s

2

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5 0
3 years ago
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valentina_108 [34]

Answer:

50

Step-by-step explanation:

To solve this problem you multiply 6 by 100 and then divide the total by 12 as follows: (6 x 100) / 12

4 0
2 years ago
Select the list that correctly includes all of the coefficients from the problem
matrenka [14]

Answer:

( B.) 6, 1, -2 , -4

Step-by-step explanation:

A coefficient is a number multiplied by a variable. So, in this case let's take a look at the problem.

-2+6y+m-2y+8-4m

Now we have to find the numbers that have a variable next to it

which are 6,m,-2, and -4

(If you are wondering that why m is a coefficient its because it is also known as 1m)

Final answer = 6, 1, -2 , -4

Hope this helps!

7 0
2 years ago
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