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artcher
1 month ago
15

A sample of size 40 is taken from an infinite population whose mean and standard deviation are 68 and 12 respectively. the proba

bility that the sample mean is larger than 70 equals:
Mathematics
1 answer:
Leona [12.6K]1 month ago
3 0

To tackle this question, we will apply the z statistic to discover the probability. The formula used for z score is:

z = (x – u) / s

Where,

u = sample mean = 68

s = standard deviation of the samples = 12

x = sample value = 70

In this instance, we want the probability that the sample mean exceeds 70, so we will look at the right side of z on the normal distribution graph.

Calculating z:

z = (70 – 68) / 12

z = 2 / 12

z = 0.17

Next, we will find P at z ≥ 0.17 using standard distribution tables:

P (z = 0.17) = 0.5675

However, this value is not our desired answer as it pertains to the left of z. Therefore, we need to compute:

P (z ≥ 0.17) = 1 - 0.5675

P (z ≥ 0.17) = 0.4325, which translates to 43.25%

 

<span>The probability that the sample mean surpasses 70 is 43.25%</span>

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Right triangle XYZ has legs of length XY = 12 and YZ = 6. Point D is chosen at random within the triangle XYZ. What is the proba
Svet_ta [12734]

The "successful" area is half the size of the overall triangle, thus using the concept of similar triangles, the likelihood that the area of triangle XYD does not exceed 12 is 1/4.

8 0
17 days ago
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The sum of four consecutive odd numbers is 368 find the numbers​
lawyer [12517]

Answer:

The four odd numbers in sequence are 89, 90, 91, and 93.

Step-by-step explanation:

Designate the four consecutive numbers as x, x+2, x+4, and x+6.

Based on the information given in the question

x + (x + 2) + (x + 4) + (x + 6) = 368

4x + 12 = 368

4x = 356

x = 89

Consequently, the numbers are 89, 90, 91, and 93.

Hope this is helpful:)

7 0
1 month ago
.580 80 repeating as fraction
Svet_ta [12734]
To start, we will shift the non-repeating segment of the decimal to the left side by dividing by a power of 10.

Then we will assign a variable to represent the value and also shift the repeating segment to the left.

Essentially, the concept here is that we can denote the repeating portion with a variable, let's say "x", and move forward with the calculation;

\bf 0.580\overline{80}\implies \boxed{\cfrac{5.80\overline{80}}{10}}\qquad \textit{now, let's say }x= 5.80\overline{80}\\\\&#10;-------------------------------

\bf thus\qquad \begin{array}{llll}&#10;100\cdot x&=&580.80\overline{80}\\&#10;&&575+5.80\overline{80}\\&#10;&&575+x&#10;\end{array}\qquad \implies 100x=575+x&#10;\\\\\\&#10;99x=575\implies x=\cfrac{575}{99}\qquad therefore\qquad \boxed{\cfrac{5.80\overline{80}}{10}}\implies \cfrac{\quad \frac{575}{99}\quad }{10}&#10;\\\\\\&#10;\cfrac{\quad \frac{575}{99}\quad }{\frac{10}{1}}\implies \cfrac{575}{99}\cdot \cfrac{1}{10}\implies \cfrac{575}{990}\implies \stackrel{simplified}{\cfrac{115}{198}}

you can verify that using your calculator.
4 0
26 days ago
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May has 4 /15 meters of lace while Lovie has 2 /7 meter longer than May's lace. how many meters of lace do girls have together​
Zina [12379]

Answer:

86/105

Step-by-step explanation:

May possesses 4/15 meters of lace

Lovie has lace that exceeds May's by 2/7 meters

4/15 + 2/7

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Consequently, the total amount of lace they have is calculated as

= 4/15 + 58/105

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8 0
1 month ago
Complete the formal proof of (~Q→~R)v(R&amp;~Q) from no premises. The empty premise line is not numbered. Hint: there are longer
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Answer:

Step-by-step breakdown:

You may consider a structure like the following while keeping in mind your specific notation.

1. | ~( (~Q ->~R) v (R & ~Q) ) Assume

2. | |  ~(~Q ->~R) Assume

3. | | |  ~(R & ~Q) Assume

4. | | |  ~R v Q    3, De Morgan

5. | | |  ~Q -> ~R 4 Material implication

6. | | |  # 2, 5 Results in a contradiction

7. | | R & ~Q 3-6 indirect proof outcome

8. | ~(~Q ->~R) ->   (R & ~Q ) 2-7 Discharging the conditional proof

9. | (~Q ->~R) v (R & ~Q) 8 Material implication derived

10 | # 1,9 Results in contradiction    

11.  (~Q ->~R) v (R & ~Q) 1-10 Completion via indirect proof

8 0
22 days ago
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