A sample from a population with μ = 40 and σ = 8 has a mean of M = 36. If the sample mean corresponds to a z = –1.00, then how many scores are in the sample?
Answer:
There are 4 scores in the sample.
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 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.
In this question, we have that:
[tex]\mu = 40, \sigma = 8, X = 36, Z = -1, s = \frac{8}{\sqrt{n}}[/tex]
We want to find n. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-1 = \frac{36 - 40}{\frac{8}{\sqrt{n}}}[/tex]
[tex]-4\sqrt{n} = -8[/tex]
[tex]4\sqrt{n} = 8[/tex]
Simplifying by 4
[tex]\sqrt{n} = 2[/tex]
[tex](\sqrt{n})^2 = 2^2[/tex]
[tex]n = 4[/tex]
There are 4 scores in the sample.
Please I need some help hereeeeeeeeee
please help me on this it is 55 points
Answer:
59/1
Step-by-step explanation:
If you borrow $3,000 at 5% simple interest for 9 months how much will you owe in 9 months? How
much interest will you pay?
Answer: $150
Step-by-step explanation:
$3,000 x 5% = 150
Mario has 6 more marbles than Sandra. Let `s` represent the number of marbles that Sandra has. Write an expression that represents the number of marbles that Mario has.
Answer:
6+s
Step-by-step explanation:
six more marbles so add 6 to s
0.8 -0.50 3 with solution
Answer:
0.3
Step-by-step explanation:
Answer:
0.8-0.503=0.297
0.8-0.50= 0.3
Step-by-step explanation:
4 5/6 + 5 7/8 please help asap tysm
Answer:
the answer to the question is 10 17/24
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the
time after launch, x in seconds, by the given equation. Using this equation, find the
maximum height reached by the rocket, to the nearest tenth of a foot.
y = -16x2 + 136x + 57
Answer:
Maximum height = 346 feet
Step-by-step explanation:
Given that,
The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation as follows :
[tex]y = -16x^2 + 136x + 57[/tex] .....(1)
We need to find the maximum height reached by the rocket. For maximum height,
Put dy/dt = 0
So,
[tex]\dfrac{d}{dt}( -16x^2 + 136x + 57)=0\\\\-32x+136=0\\\\x=\dfrac{136}{32}\\\\x=4.25[/tex]
No, put x = 4.25 in equation (1).
[tex]y = -16(4.25)^2 + 136(4.25)+ 57\\\\y=346\ feet[/tex]
So, the maximum height reached by the rocket is equal to 346 feet.
In the year 2001, a company made $5.5 million in profit. For each consecutive
year after that, their profit increased by 12%. How much would the company's
profit be in the year 2003, to the nearest tenth of a million dollars?
Which measure is equivalent to 4 feet 5 inches?
Answer:
53
Step-by-step explanation:
4ft x 12 = 48 in
48 in+ 5 in= 53
4 feet and inches will be equal to 53 inches .
Given,
4 feet 5 inches
Now conversion of inches to feet,
Few unit conversions,
Conversion Factors:
1 mile = 5280 feet
1 foot = 12 inches
1 inch = 2.54 cm
1 cm = 10 mm
1 second = 1 s
1 feet = 12 inches
Here we need to convert feet into inches,
So,
1 feet = 12 inches
4 feet = 48 inches
Hence the height will be,
48 inches + 5 inches = 53 inches
Learn more about conversions,
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#SPJ6
Can someone help quick please
Answer:
PC = 4 cm
Step-by-step explanation:
AP = 4 cm
Because AB = BC, PB = PB, and we know that angle PBA = 90 degrees: triangle PBA is congruent to triangle PBC by the Side-Angle-Side theorem.
PC = AP because corresponding parts of congruent triangles are congruent.
In which of the following expressions does the number 24 fill in the blank so that the equation is true? Select all that apply.
A) 8(3 + 5) = ___ + 40
B) 12(2 + 7) = ___ + 84
C) 8(4 + 2) = ___ + 16
D) 6(3 + 4) = 18 + ___
c
blahblahblahblahblahblahblah
cuánto es 567 + 678 es igual
Answer: 1245 :)
Step-by-step explanation:
Answer:
la respuesta es 1245
567+678=1245
Which is the volume of the solid?
Answer: the answer is A
Step-by-step explanation:
What is a common denominator?
least common denominator is the lowest common multiple of the denominators of a set of fractions. It simplifies adding, subtracting, and comparing fractions.
Answer:
12
Step-by-step explanation:
Because it is the lowest number that both 4 and 6 can reach by multiplying with whole numbers
:)
The area of the triangle below is 23.4 square inches. What is the length of the base?
6 in is the height
Answer:
543
Step-by-step explanation:
i am smart
Part 2! Please help once again! This is confusing me since I've never been good at geo. :((
Answer:
B is the answer that is incorrect and must be rejected.
Step-by-step explanation:
A trapezoidal shape need not have a line of symmetry to be a trapezoid.
2/5 - 3/5 ? Subtracting fractions
-1/5Answer:
Step-by-step explanation:
Please can someone answer this I don’t get it!!! 5 points and Brainly:)
Answer:
the answer will be 39cm yes
I need help please...............
Step-by-step explanation:
nakita ko lang po kung ayaw nyo ed don't
The size of a cell is typically found by capturing an image under a microscope then using software to measure its diameter.
Two cells are measured using this method:
Cell G: 4.21 x 10-3 centimeters
Cell H: 9.2 x 10-4 centimeters
How many times larger is the diameter of cell G than the diameter of cell H?
Write your answer in standard notation, rounding to the nearest tenth.
Answer:
Step-by-step explanation:
The answer is 6.868 10
The number of times that diameter of cell G is larger than diameter of Cell H is; 46 × 10¯¹ times
We are given;
Diameter of Cell G = 4.21 × 10^(-3) cmDiameter of Cell H = 9.2 × 10^(-4) cmNow, to find how much more larger the diameter of cell G is than diameter of cell H, we will divide the diameter of cell G by the diameter of cell H to get;
(4.21 × 10^(-3))/(9.2 × 10^(-4)) = 4.6
Thus,diameter of cell G is 4.6 times larger than diameter of Cell H
Read more about ratios at; https://brainly.com/question/2784798
At a local hardware store, Ms. Jones learned that 1 would cost her $.50, 12 would cost $1.00, and the price of 144 would be $1.50. What was Ms. Jones buying?
Answer:
how the heck would I know what she's buying the question itself doesn't even state that
you post 2 vidoes online. In the first hour video a gets 7 views video b gets 9 times as many. how many more views does video b get?
An equation is shown.
2.2 - 53 -3=0
What are the solutions to the quadratic equation?
X=
X=
The answer is -53.8
Step-by-step explanation:
jSubtract
Help please I really need it
Answer:
40%
Step-by-step explanation:
it ads up to 90, so 50+x=90 x=40
Answer:
40° as it is a right angle
then 90 - 50= 40
The invitations to a holiday party cost a total of $31.50 if each invitation cost $0.75 cents how many invitations were sent out
Answer:
42
Step-by-step explanation:
divide the total by the cost of each invite
the simplified form of (2^a)(2^b)(2^c) is
Answer:
Step-by-step explanation: hope this helps!
Solving Systems of Equations using substitution
Y= -6x - 10
Y= x + 4
I need help with this, pls put step by step
Assume that y varies inversely with x. If y = 7 when x = -2, find у when x = 7. y = ??
Answer:
-2
Step-by-step explanation:
y=k/x
Replace y with 7 and x with -2
7=k/-2 gives you -14
Then you can replace k with -14 and x with 7
y=-14/7 gives you -2