Assume that 24.5% of people have sleepwalked. Assume that in a random sample of 1478 adults, 369 have sleepwalked. a. Assuming that the rate of 24.5% is correct, find the probability that 369 or more of the 1478 adults have sleepwalked.
b. Is that result of 369 or more significantly high? c. What does the result suggest about the rate of 24.5%?
Answer:
a) 0.3483 = 34.83% probability that 369 or more of the 1478 adults have sleepwalked.
b) 369 < 403.4, which means that 369 is less than 2.5 standard deviations above the mean, and thus, a result of 369 is not significantly high.
c) Since the sample result is not significant, it suggests that the rate of 24.5% is a good estimate for the percentage of people that have sleepwalked.
Step-by-step explanation:
We use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
A result is considered significantly high if it is more than 2.5 standard deviations above the mean.
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Assume that 24.5% of people have sleepwalked.
This means that [tex]p = 0.245[/tex]
Sample of 1478 adults:
This means that [tex]n = 1478[/tex]
Mean and standard deviation:
[tex]\mu = 1478*0.245 = 362.11[/tex]
[tex]\sigma = \sqrt{1478*0.245*0.755} = 16.5346[/tex]
a. Assuming that the rate of 24.5% is correct, find the probability that 369 or more of the 1478 adults have sleepwalked.
Using continuity correction, this is [tex]P(X \geq 369 - 0.5) = P(X \geq 368.5)[/tex], which is 1 subtracted by the p-value of Z when X = 368.5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{368.5 - 362.11}{16.5346}[/tex]
[tex]Z = 0.39[/tex]
[tex]Z = 0.39[/tex] has a p-value of 0.6517
1 - 0.6517 = 0.3483
0.3483 = 34.83% probability that 369 or more of the 1478 adults have sleepwalked.
b. Is that result of 369 or more significantly high?
362.11 + 2.5*16.5346 = 403.4
369 < 403.4, which means that 369 is less than 2.5 standard deviations above the mean, and thus, a result of 369 is not significantly high.
c. What does the result suggest about the rate of 24.5%?
Since the sample result is not significant, it suggests that the rate of 24.5% is a good estimate for the percentage of people that have sleepwalked.
How many solutions would the following system of equations have? y=3x+2, and y=3x-4 is it 0, 1 or infinite ?
Choose all the expressions that are equivalent to -2(7 + -3).
A. -2 (7) + 2 (3)
B. -2(-7) - 2(3)
C. -2(7) + 2(-3)
D. -2 (7) - 2(-3)
E. -2(7) +-2(-3)
Answer:C
Step-by-step explanation:
Answer this question please ASAP!!
A or the first answer shown
Answer:
No it is not close to half of the data below the mean and half the data above the mean
Point D has coordinates (8,3). Point G has coordinates (-4,3). What is the length of segment DG?
Answer:
0
Step-by-step explanation:
Coolin
Which inequality is graphed below?
Answer:
3x-2y>6
Step-by-step explanation:
50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answer:
20?
Step-by-step explanation:
Answer: 8.9
Step-by-step explanation:
To find the hypotenuse, use the formula [tex]a^2 + b^2 = c^2[/tex]
The two "legs" are a and b (it doesn't matter which leg is a and which leg is b), but the most important thing is that the hypotenuse is c.
So, we now know that we have to solve for c. To solve for c, substitute the values shown in the image for a and b.
[tex]a^2 + b^2 = c^2[/tex]
[tex]8^2+4^2=c^2[/tex]
[tex]16 + 64 = c^2[/tex]
[tex]80 = c^2[/tex]
[tex]\sqrt{80}[/tex] = c
Use a calculator, and after rounding, you get 8.9
Plz hurry
The number of hours worked by each of the employees last week at two stores are listed below.
Vr
Hours Worked in a Week at Two Stores
Store 1
16, 28, 36, 40, 78
Store 2
22, 27, 33, 36, 40
Which statements are true and supported by the data in the table? Check all that apply.
A
2 The data for store 1 shows greater variability.
The median number of hours worked for the two stores is the same.
O The mean of the data for store 1 is greater than the mean of the data for store 2.
0 The interquartile range of both data sets is the same.
O The range
of the data for store 1 is less than the
range of the data for store 2.
Answer:
Data for store #1 shows greater variability and
The mean for store #1 is greater than the mean for store #2
Step-by-step explanation:
Answer:
a and b
Step-by-step explanation:
What is the perimeter of rectangle JKLM
Answer:
16 units
Step-by-step explanation:
m and p are complementary angles m/M = 56, and m/P = 2x + 4. Write and solve an equation to find the value of x.
WILL
GIVE BRAINLIST FOR MATH
....
A triangle has vertices of (-3,3),(-3,2), and (1,-2). What are the coordinates after dilating from the origin by a scale factor of 1/2?
Answer:
The coordinates after a dilating the triangle by a factor of 1/2 would be (-1.5, 1.5), (-1.5, 1) and (0.5, -1), respectively.
Step-by-step explanation:
Since we are dilating from the origin of the graph, (0, 0), all we need to do is multiply each vertex by the given scale factor.
Use the circle below for questions 13-16
Answer:
What circle? and where are the questions?
1 Mrs. Thiel has 178 papers to grade.
She graded 49 papers this morning
and 56 paper this afternoon. How many
papers does Mrs. Thiel have to grade
this evening?
Answer:
73 Papers
Step-by-step explanation:
Let's start by finding out how many papers Mrs. Thiel has already graded.
56 + 49 = 105
Now, let's subtract how many papers she has already graded from how many she has to grade in total.
178 - 105 = 73
So, Mrs. Thiel has to grade 73 papers this evening.
F(x) =X+4
g(x) = 3x² -7
Find (f-g) (x)
Algebra 2 sem 1
Answer:
[tex]B. ~(f+g)(x)=6x^3+4x-2[/tex]
Step-by-step explanation:
[tex]f(x)=2x^2+4x-5[/tex]
[tex]g(x)=6x^3-2x^2+3[/tex]
[tex]Find~(f+g)(x)[/tex]
[tex]=2x^2+4x-5+6x^3[/tex]
[tex]-2x^2+3[/tex]
[tex](f+g)(x)=6x^3+4x-2[/tex]
--------------------------------
hope it helps....
have a great day!!
Use OZ with VW – XY
What is XY ?
A 30
B. 35
C. 40
D 50
Answer:
40
Step-by-step explanation:
From the diagram;
VW = 2(20)
VW = 40
Simce VW is similar to XY, hence VW = XY = 40
Hence the length of XY is 40
Find the median of these numbers ? 2,7,5,4,3
Answer:
4
Step-by-step explanation:
MARK AS BRAINLIST!!
Answer:
4.
Step-by-step explanation:
The median is the 'middle number.'
In order to find the median of a data set, you must first put the numbers in numerical order.
2, 7, 5, 4, 3
↓
2, 3, 4, 5, 7
The 'middle number' in this data set is 4.
Therefore, the median is 4.
Select the correct answer from each drop-down menu.
The area of a rectangle is 91 square inches. If the length of the rectangle is 1 less than twice its width, write an equation that could be used to find the width, w, of the rectangle.
Answer:
(2w^2) + (-1w) + (-91)
Step-by-step explanation:
The equation that can be used to find the width, w, of the rectangle with the given area is: 2w² - w - 91 = 0.
What is the Area of a Rectangle?Area pf a rectangle = length × width
Given the following:
Area of rectangle = 91 in.²Width = wLength of the rectangle = 2w - 1Equation for finding w, using the area formula, would be:
(2w - 1)(w) = 91
2w² - w - 91 = 0
Therefore, the equation that can be used to find the width, w, of the rectangle with the given area is: 2w² - w - 91 = 0.
Learn more about area of rectangle on:
https://brainly.com/question/25292087
Simplify 3x^(1/2)*5x^(2/5)
Answer:
= 15x^9/10
Step-by-step explanation:
Multiply the numbers: 3 . 5 = 15
= 15x^1/2x2/5
Apply exponent rule: a^b . A^c = a^b + c
= 15x^1/2+2/5
1/2 + 2/5 = 9/10
= 15x^9/10
two congruent squares are shown in figures 1 and 2 below
Answer:
Equal to, c^2, a^2+b^2, a^2 + b^2 = c^2
Answer:
The combined area of the shaded triangles in Figure one is equal to the combined area of the shadead triangles in figure 2. The area of the unshaded square in Figure 1 can be represented by c^2. The combined area of the two unshaded squares in Figure 2 can be represented by a^2+b^2. The areas of the squares in Figure 1 and Figure 2 who that a^2+b^2=c^2.
Step-by-step explanation:
I'm right and if you think I'm wrong then you're wrong
What is the answer?
Answer:
x^2(x-5)
Step-by-step explanation:
f(x)=x-5
g(x)=x^2
g(f(x)=?
x^2(f(x)=?
x^2(x-5)
If this helps please mark as brainliest
9514 1404 393
Answer:
D. (x -5)²
Step-by-step explanation:
Replace the variable with the function argument.
G(F(x)) = G(x -5) = (x -5)² . . . . . matches choice D
Angles and are supplementary. Find the measure of angle C
Answer:
Angle C = 106 degrees
Step-by-step explanation:
I'm thinking the question should read "Angles a and C are supplementary" (software error, not yours)
Supplementary angles add up to 180 degrees
180 - 74 = 106 degrees
A wall of a building is made from blocks that are each 1 cubic foot.
The wall is 6 feet high and 6 feet wide.
A window is made by removing some blocks as shown below.
The window is 2 feet high by 2 feet wide.
The wall is 6 feet high and 6 feet wide. The window is 2 feet high by 2 feet wide is cut from the centre of the wall.
What is the volume of the wall after the window is made? Enter your answer in the box.
Answer:
6×6×1-(2×2×1)=36-4=32.
Angle measure labeled a
The arc mesure labeled c
Step-by-step explanation:
angle measure a =48/2=24°
the arc measure =360°-48°=312°
stay safe healthy and happy.Write the word sentence as an inequality a number b is less than 15
What is sin 49° to the nearest tenth?
Answer:
sin49= 0.7
Step-by-step explanation:
Question 6
What is the missing value of the following synthetic division?
Answer:
Hello!
16
Step-by-step explanation:
Because
-5+16=11
A pitcher contains 2 liters of liquid. Jin pours 368 milliliters of this liquid into a test tube.
How much liquid is left in the pitcher?
Enter your answer in the box.
Answer:
1,632 liters of liquid remain in the pitcher.
Step-by-step explanation:
Given that a pitcher contains 2 liters of liquid, and Jin pours 368 milliliters of this liquid into a test tube, to determine how much liquid is left in the pitcher the following calculation must be performed:
368 milliliters = 0.368 liters
2 - 0.368 = X
1.632 = X
Therefore, 1,632 liters of liquid remain in the pitcher.
A baker is selling pies his first customer buys 1/2 of all the pies plus 1/2 of a pie. His second customer then buys 1/2 of the pies plus 1/2 of a pie the last customer buys 1/2 of the pies plus 1/2 pie. he has no more pies. how many did he start with?
Answer:
7 pies
Step-by-step explanation:
last customer: ½+½= 1
second customer =( 1×2)+1 = 3
first customer = (3×2)+1 = 7
Question 3 of 10
On a piece of paper, graph this system of inequalities. Then determine which
region contains the solution to the system.
Answer:
Step-by-step explanation:
SEVEN