Answer:
a) 0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.
b) 0.9858 = 98.58% probability of a random sample of size 150 yielding a sample mean of between 71 and 77.
c) 0.5793 = 57.93% probability of a random sample of size 219 yielding a sample mean of less than 74.2
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 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 mean of a population is 74 and the standard deviation is 15.
This means that [tex]\mu = 74, \sigma = 15[/tex]
Question a:
Sample of 36 means that [tex]n = 36, s = \frac{15}{\sqrt{36}} = 2.5[/tex]
This probability is 1 subtracted by the pvalue of Z when X = 78. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{78 - 74}{2.5}[/tex]
[tex]Z = 1.6[/tex]
[tex]Z = 1.6[/tex] has a pvalue of 0.9452
1 - 0.9452 = 0.0548
0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.
Question b:
Sample of 150 means that [tex]n = 150, s = \frac{15}{\sqrt{150}} = 1.2247[/tex]
This probability is the pvalue of Z when X = 77 subtracted by the pvalue of Z when X = 71. So
X = 77
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{77 - 74}{1.2274}[/tex]
[tex]Z = 2.45[/tex]
[tex]Z = 2.45[/tex] has a pvalue of 0.9929
X = 71
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{71 - 74}{1.2274}[/tex]
[tex]Z = -2.45[/tex]
[tex]Z = -2.45[/tex] has a pvalue of 0.0071
0.9929 - 0.0071 = 0.9858
0.9858 = 98.58% probability of a random sample of size 150 yielding a sample mean of between 71 and 77.
c. A random sample of size 219 yielding a sample mean of less than 74.2
Sample size of 219 means that [tex]n = 219, s = \frac{15}{\sqrt{219}} = 1.0136[/tex]
This probability is the pvalue of Z when X = 74.2. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{74.2 - 74}{1.0136}[/tex]
[tex]Z = 0.2[/tex]
[tex]Z = 0.2[/tex] has a pvalue of 0.5793
0.5793 = 57.93% probability of a random sample of size 219 yielding a sample mean of less than 74.2
If an equilateral triangle has a height of 8 metres find the length of each side. Round your answer to 2 decimal places.
Answer:
9.24 m to 2 DP's.
Step-by-step explanation:
Consider the right triangle formed from a side , altitude and 1/2 the base.
By pythagoras:
x^2 = 8^2 + (0.5x)^2 where x is the length of each side.
x^2 - 0.25x^2 = 64
0.75x^2 = 64
x^2 = 64/0.75 = 85.3333.
x = 9.2376 m.
Write an equation parallel to x
– 3y = 9 that passes through the point (3,-1).
Step-by-step explanation:
x-3y=9
x=9+3y
x=12y
xy=12Tell whether – 7 is a solution of y + 14 > 2.
Answer:
y>-12
Step-by-step explanation:
y+14>2
y+14-14>2-14
y>-12
Jerry and Olivia were running a relay race. The race was 25.78 kilometers total. If Jerry ran 15.18 kilometers how far did Olivia run?
Consider the equation y = 4x - 10. Find y if x = 3.
Answer:
y = 2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
y = 4x - 10
x = 3
Step 2: Evaluate
Substitute in x: y = 4(3) - 10Multiply: y = 12 - 10Subtract: y = 2Answer:
The simplified system is the arbitrary solution of the original system of equations
Step-by-step explanation:
Y=2 and x=3
Correct me if I’m wrong.
Hope this helps
can you please help me with this? u get 15 points :))
Answer:
-80x+24
Step-by-step explanation:
At the market Sydney put a few pairs in a bag then ways the bag on a product scale the bag pairs way 4.75 pounds she adds more pairs to the bag the new way of the bag is now 5.6 pounds right and solve an addition equation to find the weight of the pairs added to the bag?
Answer:
0.85 pounds
Step-by-step explanation:
We start with a bag that weighs 4.75 pounds and want to find the weight of the pairs added to the bag.
Let x equal the weight of the pairs added to the bag.
We can write an equation containing 4.75 pounds and x, and solve for x to find this weight value.
y = 4.75 + xWe know that the final weight of the bag is 5.6 pounds, so we can substitute this value for y.
5.6 = 4.75 + xSubtract 4.75 from both sides of the equation.
0.85 = xThe weight of the pairs added to the bag is 0.85 pounds.
Elena completed the
hiking trail in 30 minutes. How many calories
did Elena burn?
Answer:
177
Step-by-step explanation:
Tom purchased 5 football games for 10.88 each and 5 pokemon games for 11.87 each with 6 20 bills. How much change did tom get
Answer:
5*10.88 + 5*11.87=113.75
120-113.75=6.25
$6.25
Step-by-step explanation:
The perimeter of a square of side 5 cm is 25 cm.
O True
O Falsethe perimeter of a circle
Answer:
false
Step-by-step explanation:
I would assume false as if each of the fours sides of the square are 5 cm, then doing the equation 5×4 (unsing 4 for the each of the congruent sides) would give up 20 cm.
write the equation below in word.
z=(8-3)+10
Answer:
I think of a number z,add 3 to it, then l subtract 8 from it.My answer is 10
Solve for the unknown in the following diagram. Round the answer to two decimal places.
in
Answer:
172.27 in
Step-by-step explanation:
Apply the Sine Rule
Sine Rule is given as:
[tex] \frac{a}{sin(A)} = \frac{b}{sin(B)} = \frac{c}{sin(C)} [/tex]
c = x = ?
C = 180 - (52 + 48) = 80° (sum of triangle)
b = 130 in.
B = 48°
Plug in the values
[tex] \frac{130}{sin(48)} = \frac{x}{sin(80)} [/tex]
Multiply both sides by sin(80)
[tex] \frac{130*sin(80)}{sin(48)} = x [/tex]
172.274641 = x
x = 172.27 in. (to 2 decimal places)
Find the value of x.
Answer:
x=20
Step-by-step explanation:
Since the sides are congruent that means the angles are congruent
When they are congruent you can equal them to each other
9x + 80 = 7x + 120
2x= 40
x=20
Math. Find Mid point and fx
Answer: Option B.
Step-by-step explanation:
When we have an interval with lower bound m and upper bound M, such that:
m ≤ x ≤ M
The mid-point is:
(m + M)/2
in this case, we have:
m = 22
M = 27
then the mid-point is:
(22 + 27)/2 = 24.5
and we know that f = 7, then:
f*x = f times the mid-point = 7*24.5 = 171.5
The correct option is B.
Two cars start towards each other from points 200 miles apart. One car travels at 40 miles
per hours and the other travel at 35 miles an hour. How far apart will the two cars be after
four hours of continuous travelling?
(a) 20
(b) 40
(c) 75
(d) 100
Answer:
D) 100
Step-by-step explanation:
Solution: After four hours, one car travels 40 x 4 = 160 km, and the other car travels 35 x 4 = 140 km. Therefore, the two cars are 160 + 140 - 200 = 100 km apart
THANK YOU
how do you simplify the fraction 5/4?
Answer:
1 1/4
Hope this helps
Answer: I think the answer is 1 1/4
Step-by-step explanation:
Need help :C
A bakery in Hong Kong regularly orders carton of cranberries from Australia. The net weight (in ounces) of
cranberries of a random sample of 20 cartons were as follow:
160 170 170 190 210 240 240 240 270 280
290 290 300 420 500 520 530 610 630 650
(c) The bakery orders the cranberries from Australia with currency exchange rate of AUD 1 to HKD 5.8.
For each ounce of Australia cranberries costs AUD 2 and the fixed shipping fee of each carton is HKD
80. Find the mean, standard deviation, range, and third quartile of the payment (in HKD) of ordering a
carton of cranberries from Australia to Hong Kong.
Answer:
i) Mean = 1933.1817
ii) Range = 5684
iii) Third quartile = 6054
Step-by-step explanation:
Given data :
currency exchange rate : 1 AUD = 5.8 HKD
cost of each ounce = 2 AUD
Fixed shipping cost for each carton = 80 HKD
number of cartons = 20
next determine the total cost of the 20 cartons in HKD
= ∑(weight in ounce * cost of each ounce *exchange rate) +fixed shipping cost
= ∑ ( 160*2*5.8 + 80 ) + -------------- + (650 *2*5.8 + 80 ) ----------------- ( 1 )
= 81756 HKD
i) find the mean value ( X )
= Total cost / number of cartons
= 81756 / 20 = 4087.8
ii) Find the standard deviation
= [tex]\sqrt{\frac{(1936-4087.8)^2+-----+(7620-4087.8)^2}{20-1} }[/tex] note: std = √∑(xi-X )^2 / (n-1)
= 1933.1817
iii) Find the range
Range = highest cost - lowest cost ( values gotten from equation 1 )
= 7650 - 1936
= 5684
iv) Determine the third quartile
third quartile = 6054
attached below is the detailed solution
Answer! If you are a bot don't even answer the question
Answer:
(x-30)/(3x-10)
Step-by-step explanation:
[tex] \frac{(x + 3)(x - 30)}{(x + 3)(3x - 10)} = \\ \frac{x - 30}{3x - 10} [/tex]
A person invests 7000 dollars in a bank. The bank pays 4% interest compounded quarterly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 14700 dollars?
Answer:
18.6
Step-by-step explanation:
Answer:
18.6
Step-by-step explanation:
trust me brotha plz give me like
Five times the difference of a number and seven is negative fifteen.
The number is ___
Answer:
Step-by-step explanation:
5*(n - 7) = - 15 Remove the brackets
5n - 35 = - 15
5n = -15 + 35
5n = 20
n = 20/5
n = 4
Answer:
4
Step-by-step explanation:
The number is 4
Assume f(x) = ax^2+ bx + c Which one is true? f is a parabola that opens sideways to the right. f is a parabola that opens sideways to the left. f is a parabola that opens downward. f is a parabola that opens upward.
Step-by-step explanation:
f is a parabola that opens upward.
please help me im literally crying help if I fail i give up i can't.
Answer:
52 m²
Step-by-step explanation:
12x3 = 36
2 x (11-3) = 2x8 = 16
36+16 = 52
Step-by-step explanation:
12 x 10 x 3 = 360
8 x 11 x 2 = 176
once you get the final amounts you add them to gather which is 536.
Hope This Helped You :)
The Venn diagram shows the relationships among different sets of numbers.
Which number would be located in the shaded part of the diagram?
-1.7
-8
2/3
10
he FDAL level for insect filth in chocolate is 0.6 insect fragments (larvae, eggs, body parts, and so on) per grams. Suppose that there is an average of 0.57 insect fragments per gram of chocolate bar and the distribution is following a Poisson distribution. Compute the probabilities that the number of insect fragments in a 50-gram sample of chocolate bar are:
Answer:
Step-by-step explanation:
[tex]\text{To find :} \\ \\ 1.) \ \ \text{More than 20} \\ \\ 2) \text{Less than 30 } \\ \\ 3) \ \text{Within the range of }( \mu - \sigma , \mu +\sigma)[/tex]
[tex]\ \ \ Since \ \ X \ \text{follows a poisson distribution and;} \\ \\ X\sim Poisson (0.57) per \ gram \\ \\ X \sim Poisson (28.5) \ per \ 50 \ grams \\ \\[/tex]
[tex]1) \ \ \ \text{The probability } P(X>20) = \sum \limits ^{50}_{x=21} \dfrac{e^{-28.5}\times 28.5^x}{x!} \\ \\ \mathbf{ = 0.9389}[/tex]
[tex]2) P( X<30) = \sum \limits ^{29}_{x=0} \dfrac{e^{-28.5}\times 28.5^x}{x!} \\ \\ \mathbf{=0.5861}[/tex]
[tex]\text{3) Since then mean}\ \mu = 28.5 \\ \\ \sigma =\sqrt{28.5} = 5.339 \\ \\ \mu - \sigma = 28.5 -5.339= 23.161 \\ \\ \mu + \sigma = 28.5 + 5.339 = 33.839[/tex]
∴
[tex]P(23.161 < X< 33.839) = \sum \limits ^{33}_{24} \dfrac{e^{-28.5}\times 28.5^x}{x! } \\ \\ = P(X\le 33) - P( X \le 23) \\ \\ = 0.82678 - 0.1750 \\ \\ \mathbf{= 0.6516}[/tex]
The ratio of blue paint to yellow paint in a green paint mixture is 2 : 3. If you use 16 ounces of blue paint, how many ounces of yellow paint do you need. Include tape diagram
Answer:
24ounces
Step-by-step explanation:
16 ounces is 2x 8
8=1:1 ratio
8x3=24
2:3 = 16:24
A person places $277 in an investment account earning an annual rate of 6.7%,
compounded continuously. Using the formula V = Pem, where V is the value of the
account in t years, P is the principal initially invested, e is the base of a natural
logarithm, and r is the rate of interest, determine the amount of money, to the
nearest cent, in the account after 10 years.
9514 1404 393
Answer:
$541.32
Step-by-step explanation:
Putting the given values into the given formula, you have ...
V = P·e^(rt)
V = $277e^(0.067·10) ≈ $541.32
ANSWER AND EXPLAIN I’LL MARK BRAINLIEST PLEASE HELP
Answer:
Im sorry I cant see the link.
Step-by-step explanation:
Answer:
x = 2
y = 1
Step-by-step explanation:
The explain in the above photo
Sorry for the little words, i will rewrite the last two rows in the comment
I hope that is useful for you
3. If an investment company pays 6% compounded semiannually, how much should you deposit
now to have $10,000 5 years from now?
Answer:
$9,287.67
Step-by-step explanation:
Number of years 5
Interest per pd 3%
FV 10,000
Calculator.net has a financial calculator that will greatly help you
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
The amount to deposits so that after 5 years, 10,000 is the amount is
$7,440.94
What is compound interest?It is the interest we earned on the interest.
The formula for the amount earned with compound interest after n years is given as:
A = P [tex](1 + r/n)^{nt}[/tex]
P = principal
R = rate
t = time in years
n = number of times compounded in a year.
We have,
r = 6%
n = 2
A = $10,000
t = 5 years
A = P [tex](1 + r/n)^{nt}[/tex]
P = 10,000 / [tex](1 + 0.03)^{10}[/tex]
P = 10,000 / [tex](1.03)^{10}[/tex]
P = $7,440.94
Thus,
The amount to deposits so that after 5 years, 10,000 is the amount is
$7,440.94
Learn more about compound interest here:
https://brainly.com/question/13155407
#SPJ2
what is 2 and 1/3 divided by 1/4
Answer:
[tex] 9\frac{1}{3} [/tex]
Find the solution to 2/3x = -24
Answer:
x=-36
Step-by-step explanation:
