The state lottery board is examining the machine that randomly picks the lottery numbers. On each trial, the machine outputs a ball with one of the digits 0 through 9 on it. (The ball is then replaced in the machine.) The lottery board tested the machine for 1000 trials and got the following results:

Outcome 0 1 2 3 4 5 6 7 8 9
Number of Trials 4 2 5 3 2 6 6 3 6 3

Required:
a. From these results, compute the experimental probability of getting an odd number.
b. Assuming that the machine is fair, compute the theoretical probability of getting an odd number.

Answer:

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation 2.

This means that [tex]\mu = 14, \sigma = 2[/tex]

Sample of 100:

This means that [tex]n = 100, s = \frac{2}{\sqrt{100}} = 0.2[/tex]

What is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2?

This is 1 subtracted by the p-value of Z when X = 14.2. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{14.2 - 14}{0.2}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a p-value of 0.8413.

1 - 0.8413 = 0.1587

0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.

Answer:

i believe its 3 but i could be wrong

Step-by-step explanation:

sorry if i am..

Answe

SI Si olla amigo lel just spammin here

Step-by-step explanation:

Answer:

Rs 440

Step-by-step explanation:

Price of bicycle = 3520

Price of mobile = 4690

Cost Price of both mobile and bicycle = 3520 + 4690

=> 8210

Selling price of both mobile and bicycle = 8650

Profit = selling price - cost price

= 8650 - 8210

= 440

Therefore he gained Rs 440

Step-by-step explanation:

[tex] \frac{135}{100} \times \frac{280}{1} = 378[/tex]

Answers:

===========================================================

Explanation:

We're given these three clues

Clue 3 is what we'll start with. Since Mrs. Gray is a doctor, this means that the doctor owns either a white horse or a brown horse. The doctor can't own a gray horse because the names can't match up (eg: the last name Gray with gray horse), due to clue 1.

If Mrs. Gray owned a brown horse, then she'd be a teacher (clue 2). But clue 3 says she's a doctor. We have a contradiction if Mrs. Gray owns the brown horse. Therefore, Mrs. Gray owns the white horse.

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

After we concluded the last section, we now know the following:

In short, we've just crossed "Mrs. Gray", "doctor", and "white horse" from the list.

Based on clue 1, we know that Mrs. Brown cannot possibly own the brown horse. Therefore, she must own the gray horse. So Mrs. White must own the brown horse.

Since Mrs. White owns the brown horse, she must be the teacher (clue 2). That leaves "lawyer" as the last profession, and that's assigned to Mrs. Brown.

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

Side note: I apologize for being a bit wordy, but I wanted to be very careful in the logical sense as to approach this problem. There's probably a much quicker efficient way to do this.

9514 1404 393

Answer:

  y +6 = 2(x -6)

Step-by-step explanation:

The slope can be found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

  m = (-4 -(-6))/(7 -6) = 2/1 = 2

The point-slope equation for a line is ...

  y -k = m(x -h) . . . . . . . line with slope m through point (h, k)

Using the slope we found and the first point, the equation is ...

  y +6 = 2(x -6)

Explanation:

Perimeter is simply the sum of all the edges. The same way 10 can be made of 4+6 or 3+7, the perimeter can be made by many combinations. if you know the 2 must equal 24cm, then we can create numerous combinations.

Answer:

[tex]cos \theta = \frac{11}{12}[/tex]

Step-by-step explanation:

[tex]sin \theta = \frac{\sqrt{23}}{12} \ , \ tan \theta = \frac{\sqrt{23}}{11}\\\\tan \theta = \frac{sin \theta }{cos \theta }\\\\ \frac{\sqrt{23}}{11} = \frac{\frac{\sqrt{23}}{12} }{cos \theta}\\\\cos \theta = \frac{\frac{\sqrt{23}}{12} }{\frac{\sqrt{23}}{11} }\\\\cos \theta = \frac{\sqrt{23}}{12 } \times \frac{11}{\sqrt{23}}\\\\cos \theta = \frac{11}{12}[/tex]

Step-by-step explanation:

Answer:

8[tex]v^{-3}[/tex]z - [tex]\frac{5}{3}[/tex] vz

Step-by-step explanation:

9514 1404 393

Answer:

  4 hours 40 minutes

Step-by-step explanation:

The appropriate relation is ...

  time = distance/speed

  time = (3800 km)/(900 km/h) +(400 km)/(900 km/h) = (38+4)/9 h

  = 14/3 h = 4 2/3 h

Seema's flight time is 4 hours 40 minutes.

__

2/3 of 60 minutes is 40 minutes

Answer:

Option (A)

Step-by-step explanation:

Sasha has an amount of $400 and saves $20 per week.

If we graph the savings of Sasha, her savings per week will be defined by the slope of the line = $20 per week

Similarly, from the graph attached,

Slope of the line given in the graph = Per week savings of Natalia

Slope of line passing through (0, 190) and (2, 210) will be,

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

          = [tex]\frac{210-190}{2-0}[/tex]

          = 10

Therefore, per week savings of Natalia = $10

Difference in savings of Sasha and Natalia = 20 - 10 = $10 per week

Here, Sasha shows the greater rate of change by $10 per week

Therefore, Option (A) will be the answer.

Answer:

77 boxes

Step-by-step explanation:

Take the total number of boxes to be sold and divide by the number of girls in the troop

1000/13

76.92307692

Round up

77

Each girl must sell 77

77*13 =1001

let the number be b

62.5/100 x b = 25

0.625 x b = 25

b =25/0.625

b=40

half of b= 40/2 = 20

11%

Hope this helps! :)

______________

Answer:

[tex] \frac{195.80}{220} \times 100 \% \\ = 0.89\%[/tex]

Step-by-step explanation:

32/3+21/5÷7

14.87÷7

2.124

Answer:

hope it helps you.......

It May Help You

Thank You:)

Answer:

336 square inches

Step-by-step explanation:

Nets are the spreaded out version/outline of 3d figures. It shows the faces of the figure. The figure in this case is actually a triangular prism.

find the area of each shape in the net:

Triangle A (1/2 x base x height)

1/2 • 8 x 6 = 24 square inches

Rectangle B (length x width):

6 x 12 = 72 square inches

Rectangle C:

8 x 12 = 96 square inches

Rectangle D:

10 x 12 = 120 square inches

Triangle E:

1/2 x 6 x 8 = 24 square inches

Add up all the areas of all shapes:

24 + 24 + 120 + 72 + 96 = 336

Surface area is measured in square inches

(Inches in this case)

Hope this helps

Hector is the one who discovered

Step-by-step explanation:

3.

1.4191919... = 1405/990

4.

√(2/5) and √(1/2)

Step-by-step explanation:

the Adjacent = √15²-9²=√225-81=√144=12

sin 0 = 9/15 = 3/5

cos 0 = 12/15 = 4/5

tan 0 = 9/12 = ¾

sec 0 = 15/12 = 5/4

csc 0 = 15/9 = 5/3

cot 0 = 12/9 = 4/3

Answer:

x=3

Step-by-step explanation:

The triangles are similar so we can use ratios to solve

x           4

----- = -----------

4.5        6

Using cross products

6x = 4.5 * 4

6x =18

Divide by 6

6x/6 = 18/6

x = 3

Answer:

Sister's house is 7.5 feet high

Step-by-step explanation:

Given :

     My house = 5  feet

     Sisters house = [tex]1\frac{2}{4}[/tex]  [tex]times[/tex]  [tex]my \ house[/tex]

                           = [tex]\frac{6}{4} \times 5[/tex]

                           [tex]=\frac{30}{4}\\\\=\frac{15}{2}\\\\= 7 . 5 \ feet[/tex]

Answer:

The last one!

Step-by-step explanation:

Answer:29.16 ml  was left

Step-by-step explanation:

2/3-3/8=

16/23-9/24=

7/24x100/1=

then divide

Answer:

Your options are not clear

Step-by-step explanation:

[tex]\sqrt[3]{-1000 \times p^{12} \times q^3} \\\\(-1 \times 10^3 \times p^{12} \times q^3)^{\frac{1}{3} }\\\\(-1^3)^{\frac{1}{3} }\times 10^{3 \times \frac{1}{3} } \times p^{12 \times \frac{1}{3}} \times q^{3 \times \frac{1}{3}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ (-1)^3 = - 1 \ ] \\\\- 1 \times 10 \times p^4 \times q\\\\-10p^4q[/tex]