Assume the average test score from the last year's class was 85 points with a standard deviation of 9. By sketching a normal curve, which value below is the best estimate for the proportion of students earned a 70 points or higher?
Answers
The given information is:
- The average test score is 85 points
- The standard deviation is 9
- It is a normal distribution
We need to find the best estimate for the proportion of students earned a 70 points or higher.
First, we need to find the z-score for 70, by applying the following formula:
[tex]z=\frac{x-\mu}{\sigma},\text{ where }\mu=average,\sigma=standard\text{ }deviation,x=value[/tex]Then, as x=70, we replace the given values and find z:
[tex]z=\frac{70-85}{9}=\frac{-15}{9}=-1.67[/tex]Then, we can find the estimate as follows:
[tex]P(X\ge70)=P(z\ge-1.67)=1-P(z<-1.67)[/tex]Now, in a standard normal table, we search the cumulative probability of z<-1.67, and it is 0.0475:
Thus, replace this value to find P(X>=70):
[tex]P(X\ge70)=1-0.0475=0.9525[/tex]The probability is 0.9525, if we multiply it by 100%, we obtain: 95.25%
The best estimate is 95%.
Related Questions
I need help with problems
Answers
Given ratio:
[tex]\frac{3}{2}\text{ : }\frac{1}{4}[/tex]Multiply both sides by the L.C.M of their denominator
The L.C.M of 2 and 4 is 4
Hence:
[tex]\begin{gathered} 4\text{ }\times\frac{3}{2}\text{ : 4}\times\frac{1}{4} \\ 6\text{ : 1} \end{gathered}[/tex]The animals at a safari park include gorillas, buffalo and wallabies. There are 24 more buffalo than there are gorillas. There are 7 times as many wallabies as there are gorillas. There are the same number of buffalo as there are wallabies. How many gorillas are there at the safari park?
Answers
The number of gorillas at the safari park is 4.
Let the number of gorillas at the safari park be x.
It is given that there are 24 more buffalo than there are gorillas.
Number of buffalo at the safari park = 24 + x
There are 7 times as many wallabies as there are gorillas.
Number of wallabies at the safari park = 7x
Now, the number of buffalo is the same as the number of wallabies.
So, we equate their numbers to find the value of x i.e. number of gorillas.
24 + x = 7x
7x - x = 24
6x = 24
x = 4
Therefore, the number of gorillas at the safari park is 4.
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tia charges a set up fee of 2$ and then 0.75 a square foot to power wash driveways which equation properly displays the amount she charges to power wash a driveway
Answers
Step-by-step explanation:
0.75x+2
2 is taken and 0.75 is not optional therfore
0.75=x(per square foot) =0.75x
and
$2 fee is required
so they must pay 2 dollars plus 0.75 everysquare foot
answer:
0.75x+2
If BC=5 in and AB=12in. Find the exact circumference of the circle.
Answers
EXPLANATION
We can get the circunference of the circle by applying the Pythagorean Theorem as shown as follows:
[tex]\text{AC}^2=AB^2+BC^2[/tex]Repalcing terms:
[tex]AC^2=12^2+5^2=144+25=169[/tex]Aplying the square root to both sides:
[tex]AC^{}=\sqrt[]{169}=13\text{ inches}[/tex]The circunference is 13 inches.
Isaac's parents borrow $3600.00 from the bank for new appliances for their kitchen. The simple interest rate is 9% per year. How much interest will they have to pay if it takes them 4 years and 3 months to repay the loan?
Answers
The interest that they will they have to pay if it takes them 4 years and 3 months to repay the loan is $1377.
How to illustrate the information?From the information, Isaac's parents borrow $3600.00 from the bank for new appliances for their kitchen and the simple interest rate is 9% per year.
Principal = $3600
Rate = 9%
Time = 4 years 3 months = 4.25
It should be noted that simple interest is calculated as:
= Principal × Rate × Time / 100
= (3600 × 9 × 4.25) / 100
= 137700 / 100
= $1377
Therefore, the interest is $1377.
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A runner has a track lap time of 1 minute while at a run, 4 minutes while at a jog, and 7 minutes while at a walk. If 2/5 of the lap is paced at a run, 1/3 at a jog, and 4/15 at a walk, what is the total track lap time of the runner? Write the solution as a mixed number or a fraction in lowest terms.
Answers
The track lap time of the runner will be 3 3/5 minutes.
How to illustrate the information?From the information, the runner has a track lap time of 1 minute while at a run, 4 minutes while at a jog, and 7 minutes while at a walk. If 2/5 of the lap is paced at a run, 1/3 at a jog, and 4/15 at a walk.
The track lap time of the runner will be:
= (2/5 × 1 minute) + (1/3 × 4 minutes) + (4/15 × 7 minutes)
Note that 1 minute = 60 seconds
(2/5 × 1 minute) + (1/3 × 4 minutes) + (4/15 × 7 minutes)
= 24 seconds + 80 seconds + 112 seconds
= 216 seconds
= 3 minutes 36 seconds.
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find the area under the standard normal curve between z=0 and z=3
Answers
The area under the standard normal curve between z=0 and z=3 is 0.4987.
How to illustrate the information?It should be noted that because the normal distribution is symmetrical on both sides of the mean and is a continuous probability distribution, the right side of the center is the opposite of the left side.
The normal distribution was first termed by early statisticians who observed that the same shape repeatedly appeared in many distributions. The characteristics of normal distributions are as follows: Bell-like in its symmetry. The distribution's mean and median, which are both at its center, are equal.
The area will be illustrated as:
P(0 < Z < 3)
From the distribution table. In this case, it's important to look at the normal distribution table under the z score for the values of zero less than Z and Z less than 3. This will be:
= 0.9987 - 0.5
= 0.4987
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What numbers are between 2/10 and 75% on a number line?
Answers
75% = 0.75
Some numbers between 0.25 and 0.75 are 0.5, 0.62, 3/10
important please help
Answers
Answer:
[tex]5 \times 10^4[/tex]
Step-by-step explanation:
Let the number of grains of rice be g.
[tex]\frac{g}{1}=\frac{1}{2 \times 10^{-5}} \\ \\ g=\frac{1}{2} \times 10^5 \\ \\ =5 \times 10^4[/tex]
My little sister decided that she had to have a new Softball so she went to the bank where she holds her money and emptied it out completely in order to get my recent need it for the ball the money was in the form of 45 coins with me your personal little heavy for her to carry and also took a long time for her to come out the money at the store I had to take her and I got bored wedding how many pennies nickels dimes quarters and a half dollars did she have with her
Answers
Answer:
you know it's a very good question
Step-by-step explanation:
I have no idea
If jack drives 876 miles to Mexico Tuesday, and 986 miles wens day , what-is the total miles he drove?
Answers
The distance travelled by Jack to Mexico on Tuesday is 876 miles.
The distance travelled by Jack to Mexico on Wednesday is 986 miles.
To determine the total miles he drove ,
The sum of the distance travelled by Jack to Mexico on Tuesday and Wednesday.
Let the total miles drove is denoted as T.
[tex]T=876+986[/tex][tex]T=1862\text{ miles.}[/tex]Thus the total miles drove is 1862 miles.
A house purchased for $265,100 gains 2% of its value every year. If this growth rate continues, in how many years will the house be worth twice its original value
Answers
The price of the house will double the original value in 35 years
How to determine the number of years?The given parameters from the question are
Initial value of the house = $265,100
Rate of gain = 2% of its value every year
An exponential function is represented as
y = a *(1 + r)^x
Where
y represents the current valuea represents the initial valuer represents the growth or decay ratex represents the number of years, in this caseThis means that
a = 265,100
r = 2%
So, we have
y = 265,100 *(1 +2%)^t
When the price doubles, we have
2 * 265,100 = 265,100 *(1 +2%)^t
Divide both sides by 265,100
So, we have
2 = (1 +2%)^t
Evaluate the sum
So, we have
2 = 1.02^t
Take the logarithm of both sides
t * log(1.02) = log(2)
Divide
t = log(2)/log(1.02)
Evaluate
t = 35
Hence, the number of years is 35
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$15 per hour is the basic rate at a factory. After a 48-hour basic work week, overtime is paid time and a half.
(a) If no one worked overtime and the factory paid $15 840 in wages one week, how many workers are in the factory?
(b) During another week, a worker in the factory earns $810 in wages for himself. How many hours did he work for?
Answers
Answer:
(a) There are 22 workers are available in the factory.
Step-by-step explanation:
(a) Let the number of workers in the factory be x.
Basic rate = $15
Working hours in a week = 48 hours
Total wages in a week = $ 15840
If no overtime is to be paid then according to question,
Amount paid to 1 worker = 48 X 15 = $ 720
Amount paid to x worker = 720x
15840 = 720
x = 15840/720
x = 22
Solve for x to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
first from the lower triangle, the unknown length is [tex]\sqrt{10^2-4^2} =\sqrt{100-16}=\sqrt{84}[/tex] so then x is equal to [tex]\sqrt{84-4^2}=\sqrt{68}[/tex] or about 8.2
Please help I’ll mark you as brainliest if correct!!
Answers
(Look at picture) 8th grade pre-algebra math question, super easy!
Answers
The true statements about the solutions to this number line include the following:
A. -1 is a solution.
E. -1.5 is a solution.
F. All negative numbers are solutions.
What is a number line?A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numbers (numerical values) that are placed at equal intervals along its length.
This ultimately implies that, a number line can be used to determine the difference between two numbers such as 23 and 12. Also, a number line typically increases in numerical value towards the right and decreases in numerical value towards the left.
In conclusion, we can reasonably infer and logically deduce that an inequality which represent the solutions to this number line in interval notation is given by: -1 ≤ x ≤ ∞.
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need help answering
Answers
ieven
raph of the fucnction
ind
quation of the fuctcion
xpolanation
s we see it i s the graph of exponential function.
from graph we find point (0 , 2)
now , we substitute this point to find the equation.
[tex]\begin{gathered} y=0.5^x+1 \\ y=0.5^0+1 \\ y=1+1 \\ y=2 \end{gathered}[/tex]so , this exponential function satisfy the point.
Final Answer
ence , the correct option is 1,.
one hundred and twenty one million, two hundred and twelve thousand and eighty-eight in number
Answers
Complete the frequency table for the following set of data. =
Answers
Given the set of data:
12, 4, 11, 3, 4, 0, 13, 13, 2, 6, 11, 0, 10, 11, 3, 4, 0, 10, 13, 2, 11, 9.
Let's complete the given frequency table using the set of data given.
Frequency can be said to be the number of times a number occurs in a set of data.
hus, we have:
• 0 - 2
ubmbers between 0 - 2 in the data set: 0, 2, 0, 0, 2 ==> 5 times
• 3 - 5
3 - 5: 4, 3, 4, 3, 4, ==> 5 times
• 6 - 8:
6 - 8: 6, ==> 1 time
• 9 - 11:
: 9 - 119, 11, 11, 10, 11, 10, 11, 9 ==> 7 times
• 12 - 14:
12 - 134: 12, 13, 13, 13 =3 ==> 4 times.
Therefore, the complete table is:
On your own paper, graph the system of equations and identify the solution.=2−4=−12+1
Answers
The Slope-Intercept Form of the equation of a line is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
You have the first line:
[tex]=2x-4[/tex]You can identify that the y-intercept is:
[tex]b_1=-4[/tex]You can find the x-intercept substituting the following value of "y" into the equation of the line:
[tex]y=0[/tex]And, after the substitution, you can solve for "x":
[tex]\begin{gathered} 0=2-4 \\ 4=2x \\ \\ \frac{4}{2}=x \\ \\ x=2 \end{gathered}[/tex]Now you know that the first line passes through these points:
[tex]\begin{gathered} (0,-4) \\ (2,0) \end{gathered}[/tex]Then, you can graph it.
Given the second line:
[tex]y=-\frac{1}{2}x+1[/tex]You can identify that:
[tex]b_2=1[/tex]And you can find the x-intercept by following the same procedure applied for the first line:
[tex]\begin{gathered} 0=-\frac{1}{2}x+1 \\ \\ -1=-\frac{1}{2}x \\ \\ (-1)(2)=-x \\ \\ -2=-x \\ x=2 \end{gathered}[/tex]Then, this line passes through these points:
[tex]\begin{gathered} (0,1) \\ (2,0) \end{gathered}[/tex]Now you can graph it.
See the graph below:
By definition, when the lines intersect, the solution of the System of equations is the point where the two lines intersect.
The answer is: First option.
Please help me help help me please help help me
Answers
ANSWER
t = 10.27
EXPLANATION
Step 1: Given
[tex]500e^{0.0675t}\text{ = 1000}[/tex]Step 2: Divide both sides by 500
[tex]\begin{gathered} \frac{500e^{0.0675t}}{500}\text{ = }\frac{1000}{500} \\ e^{0.0675t}\text{ = }2 \end{gathered}[/tex]Step 3: Take the natural logarithm of both sides
[tex]\begin{gathered} 0.0675t\text{ = ln 2} \\ 0.0675t\text{ = }0.69314718056 \end{gathered}[/tex]Step 4: Divide both sides by 0.0675
[tex]\begin{gathered} \frac{0.0675t}{0.0675}\text{ = }\frac{0.69314718056}{0.0675} \\ t\text{ = 10.268847} \end{gathered}[/tex]Hence, t = 10.27 (rounded to the nearest hundredth).
Help ASAP solve for the value of Z
Answers
Answer:
z = 6
Step-by-step explanation:
The angle in the middle is a right angle with a measure of 90°
Together, all three angles, makes a stright angle which is measured 180°.
So we can write the following equation to find the value of z:
5z + 1 + 59 = 90 (we don'thave to include the middle angle since we already its measure)
add like terms
5z + 60 = 90 subtract 60 from both sides
5z = 30 divide both sides by 5
z = 6
What does standard deviation measure in a probability distribution?
Answers
Answer:
omg what is standard deviation that was on my psat today
Slope intercept form for points through (0,-4) and (2,1)
Answers
Answer:
y = (5/2)x - 4
Step-by-step explanation:
(0, -4) and (2, 1)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 1 - (-4) 1 + 4 5
m = ------------- = ------------ = --------- = --------
x₂ - x₁ 2 - 0 2 2
y - y₁ = m(x - x₁)
y - (-4) = (5/2)(x - 0)
y + 4 = (5/2)x - 0
-4 -4
----------------------------
y = (5/2)x - 4
I hope this helps!
1. Identify 4x + 2(x -6) = 7 as an equation, an expression, or neither A. Expression B. Equation C. Neither
Answers
Answer:
Equation
Step-by-step explanation:
Equations require equal signs.
20% plain M&Ms are orange. Sample of 100 candies randomly selected. Find the man and standard deviation
Answers
Answer: μ=20, σ=4.0
Step-by-step explanation:
The tutorial doesn't say anything about this and I need help. What is the slope and how do you find it
Answers
Answer:
i cannot see the lines very well, but i can tell you how to find slope
Step-by-step explanation:
slope is rise/run. find where the line hits a intersection on the graph, and count the squares across the graph where it hits another intersection. it should not be on the line though, because that is only the run. then count how many squares up it takes till you touch where the line hits another intersection. that is the rise. then divide the rise by the run.
What are all the solutions, both real and nonreal, to 4x3 + 96x = 0?
Answers
Answer:
it is 1,152
Step-by-step explanation:
4×3=12×96=1,152
Answer:a
Step-by-step explanation:
Josh's mom gave him money to spend at an
amusement park. So far, he's used 3/10 of the
money on games and 1/4 of the money on rides.
What fraction of the money does he have left?
Give your answer as a fraction in simplest form.
Answers
Answer:
9/20
Step-by-step explanation:
3/10 + 1/4
find a common denominator, which is 20 here
6/20 + 5/20 = 11/20 he used
left over is 9/20
Divide. Express your answer in scientific notation.
8.1×10^−7
3×10^−3
Answers
[tex]\frac{2.4}{10^{4} }[/tex] is the simplest form of scientific notation.
What is notation?In mathematical notation, operations, unnamed numbers, relations, and any other mathematical objects are represented by symbols that are combined into expressions and formulae. Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation. For instance, 650,000,000 can be expressed as 6.5 108 in scientific notation. A system of symbols for designating unique items. Example: In mathematics, the symbol "∞" stands for "infinity." There are many notations in mathematics.
Given Data
8.1×10^−7
3×10^−3
Dividing
[tex]\frac{8.1(10}{3(10}[/tex]⁷₃
[tex]\frac{8.1}{3}[/tex] × 10⁻⁷⁻⁽⁻³⁾
2.7 × 10⁻⁴
[tex]\frac{2.4}{10^{4} }[/tex]
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