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Cerrena [4.2K]
3 years ago
14

Maple tree diameters in a forest area are normally distributed with mean 10 inches and standard deviation 2.2 inches. Find the p

roportion of trees having a diameter less than 9 inches.
Mathematics
1 answer:
Mila [183]3 years ago
4 0

Answer:

0.32472

Step-by-step explanation:

Maple tree diameters in a forest area are normally distributed with mean 10 inches and standard deviation 2.2 inches. Find the proportion of trees having a diameter less than 9 inches.

The formula for calculating a z-score is z = (x-μ)/σ

where x is the raw score

μ is the population mean

σ is the population standard deviation

z = (9 - 10)/2.2

z = -1/2.2

= -0.45455

Probability value from Z-Table:

P(x ≤ 9) = P(x < 9)

= 0.32472

Therefore, the proportion of trees having a diameter less than 9 inches is

0.32472

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If the Captain and the pirate each shoot once, and the Captain shoots first, what is the probability that the Captain hits the p
OLga [1]

Answer:

50/50

Step-by-step explanation:

3 0
4 years ago
A second particle, Q, also moves along the x-axis so that its velocity for 0 £ £t 4 is given by Q t cos 0.063 ( ) t 2 v t( ) = 4
Vladimir79 [104]

Answer:

The time interval when V_Q(t) \geq 60  is at  1.866 \leq t \leq 3.519

The distance is 106.109 m

Step-by-step explanation:

The velocity of the second particle Q moving along the x-axis is :

V_{Q}(t)=45\sqrt{t} cos(0.063 \ t^2)

So ; the objective here is to find the time interval and the distance traveled by particle Q during the time interval.

We are also to that :

V_Q(t) \geq 60    between   0 \leq t \leq 4

The schematic free body graphical representation of the above illustration was attached in the file below and the point when V_Q(t) \geq 60  is at 4 is obtained in the parabolic curve.

So, V_Q(t) \geq 60  is at  1.866 \leq t \leq 3.519

Taking the integral of the time interval in order to determine the distance; we have:

distance = \int\limits^{3.519}_{1.866} {V_Q(t)} \, dt

= \int\limits^{3.519}_{1.866} {45\sqrt{t} cos(0.063 \ t^2)} \, dt

= By using the Scientific calculator notation;

distance = 106.109 m

4 0
3 years ago
Enrique left the study group traveling 20 mph. Then, 2 hours later, Tevin left traveling the same direction at 28 mph. How long
nadya68 [22]

Answer:

After 7 hours Tevin will catch Enrique

Step-by-step explanation:

We have given speed of Enrique is 20 mph

Tevin left traveling after 2 hours of Enrique

Speed of Tevin  is 28 mph

When Tevin catches  Enrique will cover same distance

Let  Enrique is traveling for t hours

Then Tevin will travel for t-2 hours

We know that distance = speed × time

So 20\times t=28\times (t-2)

20t=28t-56

8t=56

t = 7 hours

So after 7 hours Tevin will catch Enrique

4 0
4 years ago
Which of the following choices is the standard deviation of the sample shown
frozen [14]

Answer:

Mean = (19 + 20 + 21 + 22 + 23)/5 = 105/5 = 21

x    x - mean   (x - mean)^2

19     -2                4

20     -1                1

21      0                0

22      1                1

23      2                4

              Sum = 10

Step-by-step explanation:

7 0
4 years ago
Brianna received an overall IQ score of 117 on the Wechsler Scale. This means that Brianna has scored approximately____________
Tresset [83]

Using the normal distribution, it is found that the correct option is:

  • D. 1; 100

In a <em>normal distribution</em> with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • It measures how many standard deviations the measure is from the mean.

In this problem:

  • The mean on the Wechsler Scale is of 100, hence \mu = 100.
  • The standard deviation is of 17, hence \sigma = 17.
  • Brianna had an score of 117, hence X = 117

Then:

Z = \frac{X - \mu}{\sigma}

Z = \frac{117 - 100}{17}

Z = 1

Hence, the option d is correct.

To learn more about the normal distribution, you can check brainly.com/question/24663213

7 0
3 years ago
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