Answer:
0.001 = 0.1% probability that a sample of this size would have a mean of 64.82 inches or less.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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.
Central Limit Theorem
The Central Limit Theorem estabilishes 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 heights of adults in a certain town have a mean of 65.42 inches with a standard deviation of 2.32 inches.
This means that [tex]\mu = 65.42, \sigma = 2.32[/tex]
Sample of 144:
This means that [tex]n = 144, s = \frac{2.32}{\sqrt{144}} = 0.1933[/tex]
Find the probability that a sample of this size would have a mean of 64.82 inches or less.
This is the pvalue of Z when X = 64.82. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{64.82 - 65.42}{0.1933}[/tex]
[tex]Z = -3.1[/tex]
[tex]Z = -3.1[/tex] has a pvalue of 0.001
0.001 = 0.1% probability that a sample of this size would have a mean of 64.82 inches or less.
Mr. Rich has 75 papers. He graded 60 papers, and he had a student teacher grade the rest. What percent of the papers did each person grade?
Please help me ASAP
Answer:
Mr. Rich did 80% and the student did 20%
Step-by-step explanation:
60/75 = 80%
15/75 = 20%
si el peso de la figura es de 80 N cuales son las tensiones en las cuerdas a y b
Answer: Can you translate for me? I don't know spanish.
Step-by-step explanation:
:)
F(-1)=4-3x
F(2)=4-3x
Help me pls pls pls
Answer:
hdjdndjbzsbshsbs sbsbsbs
student book grade 5 page 87
Answer:
Brainly isn't for answer keys... It's to help you understand how to do something better or just how to do it in general.
Step-by-step explanation:
Very Easy will give brainlist Find The Length put image below
Answer:
The answer should be G
Step-by-step explanation:
Hope this helps.
Have a great day
Answer the question plz
Answer:
1) A- 95
2) B- 125
Step-by-step explanation:
1) 50 + 35+x = 180
85 +x = 180
x = 180- 85
= 95
2) 70 +80 + 85+d = 360
235 + d = 360
d = 360 - 235 = 125
I Hope im right!
what is the surface area of a cube with the dimensions of 3in by 3in by 3in?
Answer:
54
Step-by-step explanation:
Find the distance on the graph
what is 1 4/5 + (-3 4/10) show your work !
Answer:
[tex]-\frac{8}{5} = -1\frac{3}{5}[/tex]
Step-by-step explanation:
[tex]1 \frac{4}{5} = \frac{9}{5}[/tex]
[tex]-3 \frac{4}{10} = -\frac{34}{10} = -\frac{17}{5}[/tex]
Multiply the whole number by the denominator and add that to the numerator. I simplified [tex]-\frac{34}{10}[/tex] by dividing by two getting [tex]-\frac{17}{5}[/tex]. Then add [tex]\frac{9}{5}[/tex] and [tex]-\frac{17}{5}[/tex] together. Then put [tex]-\frac{8}{5}[/tex] into a mixed fraction. How many times does 5 go into 8 and what is the remainder? The answer is -1 times and the remainder is 3. The mixed fraction is [tex]-1 \frac{3}{5}[/tex].
The expression 1 4/10 + (-3 4/10 gives the value -1 3/5.
What are Mixed Fractions?Mixed fractions are type of fractions which consist of a whole number part and a fractional part.
Mixed fractions are of the form a b/c where a is the whole number part and b/c is the fractional part.
Given expression is,
1 4/5 + (-3 4/10)
Since a positive and negative combined, it becomes negative.
Also mixed fractions can be converted into improper fractions.
1 4/5 + (-3 4/10) = 1 4/5 - 3 4/10
= [(1 × 5 + 4) / 5] - [(3 × 10 + 4) / 10]
= (9 / 5) - (34 / 10)
Making the denominator of first fraction equal by multiplying with 2 on both numerator and denominator,
1 4/5 + (-3 4/10) = [(9 × 2) / (5 × 2)] - [34 / 10]
= (18 / 10) - (34 / 10)
= -16 / 10
= -1 6/10
= -1 3/5
Hence the value of the expression is -1 3/5.
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Last week a pound of grapes cost $3. This week they are 12% more expensive.
What is the current price of a pound of grapes?
Enter your answer in the box
Answer:
3.36
Step-by-step explanation:
3+12%=3.36
Is a coin flip random? Why or why not, in your opinion?
Choose the correct answer below.
A.
Yes. You will get heads on every other flip.
B.
Yes. You cannot predict the outcome beforehand.
C.
No. You must run numerous trials before you can tell.
D.
No. You can predict the outcome beforehand.
Answer:
B
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
If sally had two apples and jerry have her 5 more how many does she have now.
Answer:
7
Step-by-step explanation:
2 + 5 = 7
Calculate the length of the diagonal AB
Answer:
AB = [tex]5\sqrt{3}[/tex] cm
Step-by-step explanation:
The diagonal of the bottom square is the hypotenuse of two right triangles with legs 5 and 5
So, the length of that diagonal, say x, of a 45-45-90 triangle where x is the hypotenuse is x = [tex]5\sqrt{2}[/tex]
Now that diagonal is a leg of the right triangle where AB is the hypotenuse and 5 is the length of the other leg.
So, [tex]x^{2} + 5^{2} = AB^{2}[/tex] = [tex](5\sqrt{2} )^{2}[/tex] + 25
= 50 + 25
= 75
Therefore AB = [tex]\sqrt{75}[/tex] = [tex]5\sqrt{3}[/tex]
r+4 at r=13 help me
The value of the expression is 17.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
r + 4
When r = 13
r + 4
= 13 + 4
= 17
Thus,
The value is 17.
Learn more about expressions here:
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Find the Simple Interest
$700 deposited at an interest rate of 1.5% for 3 years
Answer:
$31.50
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 1.5%/100 = 0.015 per year,
then, solving our equation
I = 700 × 0.015 × 3 = 31.5
I = $ 31.50
The simple interest accumulated
on a principal of $ 700.00
at a rate of 1.5% per year
for 3 years is $ 31.50.
3 1/5 x 4 1/2 ayuda por favor
Answer:
14 2/5
Step-by-step explanation:
The manager of a furniture factory finds that it costs $2400 to manufacture 60 chairs in one day and $4800 to produce 260 chairs in one day.
A) Express the cost C (in dollars) as a function of the number of chairs x produced, assuming that it is linear.
B. What is the slope of the graph? What does it represent?
C) What is the y-intercept of the graph? What does it represent?
Answer:
C(x) = 12x + 1680
Slope = 12
Intercept = 1680
Step-by-step explanation:
Given that:
X1 = 60 chairs ; y1 = 2400
X2 = 260 chairs ; y2 = 4800
Obtain the slope ; m
m = y2 - y1 / x2 - x1
m = 4800 - 2400 / 260 - 60
m = 2400 / 200
m = 12
Using the point slope relation:
y - y1 = m(x - x1)
y - 2400 = 12(x - 60)
y - 2400 = 12x - 720
y = 12x - 720 + 2400
y = 12x + 1680
C(x) = 12x + 1680
From the general slope intercept equation :
y = mx + c
m = slope ; c = intercept
Hence,
C(x) = 12x + 1680
Slope = 12
Intercept = 1680
I only need the answer FAST!!
Answer:
d.
Step-by-step explanation:
Answer:
2 points per minute is a required answer
The coordinates of point T are (0,4). The midpoint of ST is (5,-7). Find the coordinates of point S.
Answer:
(10, -18)
Step-by-step explanation:
midpoint formula: (sum of both x-values/2, sum of both y-values/2)
(0 + x)/2 = 5
x = 10
(4 + y)/2 = -7
y = -18
1 Frederick planted a tree in his backyard. He is 6 feet tall and his shadow along the ground has a length of 8 feet. The tree is currently casting a shadow along the ground that has a length of 24 feet. How tall is the tree?
Answer:
72 ft. 6ft x8ft +24=72 ft
За + 4 = 25 whats the answer
Answer: 7
Step-by-step explanation:
3a + 4 = 21
Step 1 subtract 4 from both sides.
3a+4−4=25−4
3a = 21
Step 2: Divide both sides by 3.
3a / 3 = 1
21 / 3 = 7
a = 7
t x 3/4 for t =8/9 i don't know it
Answer:
2/3
Step-by-step explanation:
8/9 x 3/4 = 2/3 x 1/1 = 2/3
HELP PLEASE ILL GIVE YOU BRAINLEST IF U GIVE ME THE CORRECT ANSWER FOR THE QUESTION IN THE PIC
Answer:
b. f(3.5) = 52
Hope this helps!
Katie got a loan for $10,000. The interest rate is 5%. How much interest will she pay in one year?
Answer: 10,000 x 0.05 = $500
0.05 is equal to 5%
$500
Please brainlyist
$75 is divided into 5 piles how much in each pile
Answer:
15
Step-by-step explanation:
75/5=15
Answer: 15 dollars in each pile.
Step-by-step explanation:
Since there is 75 in total, and we have to divide the 75 equally between the 5 piles, we can use the division equation: 75 / 5.
75 / 5 = 15.
Therefore, there will be 15 dollars in each pile. Hope this helps and good luck!
PLZ HURRY IT'S URGENT!!!
What are the roots of the quadratic graphed?
-4 and 3
-3 and 4
0 and -6
0 and 6
the answer is -4 and 3
hope that helped
Andre is making paper cranes to decorate for a party. He plans to make one large paper crane for a centerpiece and several smaller paper cranes to put around the table. It takes Andre 10 minutes to make the centerpiece and 3 minutes to make each small crane. He will only have 30 minutes to make the paper cranes once he gets home.
Andre wrote the inequality 3x+10≤30 to plan his time.
Solve Andre’s inequality.
What is X?
Answer:
Andre can make 6 small paper cranes in 30 minutes.
Step-by-step explanation:
Simplify the expression. -3(1+n)-6n
Answer:
− 3 − 9 n
Step-by-step explanation:
Simplify the expression
what is 35 degrees in one second
Answer:
35.0169°
Step-by-step explanation:
35.0169°
I hope this helps you!!