Answer:
0.9974 = 99.74% probability of selecting a sample of 65 one-bedroom apartments and finding the mean to be at least $2,260 per month.
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.
The rent for a one-bedroom apartment in Southern California follows the normal distribution with a mean of $2,350 per month and a standard deviation of $260 per month.
This means that [tex]\mu = 2350, \sigma = 260[/tex]
Sample of 65 one-bedroom apartments
65>30, which means that the sampling distribution of the sample means will be approximately normal. Also, [tex]n = 65, s = \frac{260}{\sqrt{65}} = 32.249[/tex]
What is the probability of selecting a sample of 65 one-bedroom apartments and finding the mean to be at least $2,260 per month?
This is 1 subtracted by the pvalue of Z when X = 2260.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{2260 - 2350}{32.249}[/tex]
[tex]Z = -2.79[/tex]
[tex]Z = -2.79[/tex] has a pvalue of 0.0026
1 - 0.0026 = 0.9974
0.9974 = 99.74% probability of selecting a sample of 65 one-bedroom apartments and finding the mean to be at least $2,260 per month.
PRETTY MUCH A FREE BRAINLIEST IF UR RIGHT, GOOD LUCK :D. Value of x is greater than or equal to 14
Options:
x>14
x<14
x≥14
x≤14
Answer:
3rd choice down. . . . . . .
x≥14 plz give me brainlyest
Consider the expression 40+24 . Find the greatest common factor of the two numbers and use the distributive property to rewrite the expression
Hi there!
[tex]\large\boxed{8(5+3)}}[/tex]
The greatest common factor of 40 and 24 is 8.
8 goes into 40 5 times:
8 goes into 24 3 times.
We can rewrite this expression for distribution using the amount of times 8 goes into both numbers:
8(5 + 3)
Using this, we get:
8(5) + 8(3) = 40 + 24.
A store sells 8 colors of balloons with at least 28 of each color. How many different combinations of 28 balloons can be chosen? Apply the method of Example 9.6.2 using balloons instead of cans of soft drinks to find that the number of different combinations of 28 balloons that can be chosen is . (b) If the store has only 12 red balloons but at least 28 of each other color of balloon, how many combinations of balloons can be chosen? Use the method of Example 9.6.2(c) to answer this question. If the store has only 12 red balloons, then the number of different selections of 28 balloons of the different colors is the same as the number of different selections that contain 12 or fewer red balloons. Let T be the set of all possible selections, assuming that there are at least 28 balloons of each type, let R≤12 be the set of selections in T that contain 12 or fewer red balloons, and let R≥13 be the set of selections from T that contain 13 or more red balloons. Use the relationships among R≤12, R≥13, and T to find that the number of different combinations of 28 balloons that can be chosen is . (c) If the store has only 8 blue balloons but at least 28 of each other color of balloon, how many combinations of balloons can be chosen? (d) If the store has only 12 red balloons and only 8 blue balloons but at least 28 of each other color of balloon, how many combinations of balloons can be chosen?
Answer:
(a) [tex]Selection = 6724520[/tex]
(b) [tex]At\ most\ 12 = 6553976[/tex]
(c) [tex]At\ most\ 8 = 6066720[/tex]
(d) [tex]At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 5896638[/tex]
Step-by-step explanation:
Given
[tex]Colors = 8[/tex]
[tex]Balloons = 28[/tex] --- at least
Solving (a): 28 combinations
From the question, we understand that; a combination of 28 is to be selected. Because the order is not important, we make use of combination.
Also, because repetition is allowed; different balloons of the same kind can be selected over and over again.
So:
[tex]n => 28 + 8-1[/tex][tex]= 35[/tex]
[tex]r = 28[/tex]
[tex]Selection = ^{35}^C_{28[/tex]
[tex]Selection = \frac{35!}{(35 - 28)!28!}[/tex]
[tex]Selection = \frac{35!}{7!28!}[/tex]
[tex]Selection = \frac{35*34*33*32*31*30*29*28!}{7!28!}[/tex]
[tex]Selection = \frac{35*34*33*32*31*30*29}{7!}[/tex]
[tex]Selection = \frac{35*34*33*32*31*30*29}{7*6*5*4*3*2*1}[/tex]
[tex]Selection = \frac{33891580800}{5040}[/tex]
[tex]Selection = 6724520[/tex]
Solving (b): At most 12 red balloons
First, we calculate the ways of selecting at least 13 balloons
Out of the 28 balloons, there are 15 balloons remaining (i.e. 28 - 13)
So:
[tex]n => 15 + 8 -1 = 22[/tex]
[tex]r = 15[/tex]
Selection of at least 13 =
[tex]At\ least\ 13 = ^{22}C_{15}[/tex]
[tex]At\ least\ 13 = \frac{22!}{(22-15)!15!}[/tex]
[tex]At\ least\ 13 = \frac{22!}{7!15!}[/tex]
[tex]At\ least\ 13 = 170544[/tex]
Ways of selecting at most 12 =
[tex]At\ most\ 12 = Total - At\ least\ 13[/tex] --- Complement rule
[tex]At\ most\ 12 = 6724520- 170544[/tex]
[tex]At\ most\ 12 = 6553976[/tex]
Solving (c): At most 8 blue balloons
First, we calculate the ways of selecting at least 9 balloons
Out of the 28 balloons, there are 19 balloons remaining (i.e. 28 - 9)
So:
[tex]n => 19+ 8 -1 = 26[/tex]
[tex]r = 19[/tex]
Selection of at least 9 =
[tex]At\ least\ 9 = ^{26}C_{19}[/tex]
[tex]At\ least\ 9 = \frac{26!}{(26-19)!19!}[/tex]
[tex]At\ least\ 9 = \frac{26!}{7!19!}[/tex]
[tex]At\ least\ 9 = 657800[/tex]
Ways of selecting at most 8 =
[tex]At\ most\ 8 = Total - At\ least\ 9[/tex] --- Complement rule
[tex]At\ most\ 8 = 6724520- 657800[/tex]
[tex]At\ most\ 8 = 6066720[/tex]
Solving (d): 12 red and 8 blue balloons
First, we calculate the ways for selecting 13 red balloons and 9 blue balloons
Out of the 28 balloons, there are 6 balloons remaining (i.e. 28 - 13 - 9)
So:
[tex]n =6+6-1 = 11[/tex]
[tex]r = 6[/tex]
Selection =
[tex]^{11}C_6 = \frac{11!}{(11-6)!6!}[/tex]
[tex]^{11}C_6 = \frac{11!}{5!6!}[/tex]
[tex]^{11}C_6 = 462[/tex]
Using inclusion/exclusion rule of two sets:
[tex]Selection = At\ most\ 12 + At\ most\ 8 - (12\ red\ and\ 8\ blue)[/tex]
[tex]Only\ 12\ red\ and\ only\ 8\ blue\ = 170544+ 657800- 462[/tex]
[tex]Only\ 12\ red\ and\ only\ 8\ blue\ = 827882[/tex]
[tex]At\ most\ 12\ red\ and\ at\ most\ 8\ blue = Total - Only\ 12\ red\ and\ only\ 8\ blue[/tex]
[tex]At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 6724520 - 827882[/tex]
[tex]At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 5896638[/tex]
During a competition, numismatist Aditi has been given Rs. 200 in Rs.1 denominations. The judge asks Aditi to allocate the Rs. 1 denominations into a number of pouches such that any amount required between Rs.1 & Rs. 200 can be given by giving out a certain number of pouches without opening them. Aditi thinks and asks the judge to give her 'x' number of pouches to keep the money, where 'x' is the minimum number of bags required to keep the total money. Can you guess the value of 'x'?
9514 1404 393
Answer:
8
Step-by-step explanation:
If the bags can either be given or not, each bag can assume one of two states. In order for there to be 200 possible combinations of items in one of two states, there must be at least log2(200) = 7.64 items. The minimum number of bags is x = 8.
_____
The contents of the 8 bags will be Rs. 1, 2, 4, 8, 16, 32, 64, 73.
Please help, will give brainliest! Which is NOT equivalent to this expression? 4(3x^2+6x)
A. one solution
B. infinitely many solutions
C. no solution
19.214÷13
pls someone help me
Answer:
1.478
Step-by-step explanation:
Find the measure of the arc.
D
А
146°E
B
mĒDF = [?]°
Enter
Answer: 214
hope this helped.
The measure of the arc is 214 degrees
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
The measure of the arc FE is 146 degrees.
Measure ED is 90 degrees.
To find the measure of the arc EDF we have to find the measure of DF.
146+90+x=360
236+x=360
Subtract 236 from both sides
x=360-236
x=124
Now let us find the arc measure EDF =Measure of ED + Measure of DF
=90+124
=214 degrees
Hence, the measure of the arc is 214 degrees
To learn more on Circles click:
https://brainly.com/question/11833983
#SPJ7
If you are given the diameter, how can you calculate the radius
Answer:
divide the diameter by 2
The owner of a restaurant is concerned about customers who ask for a water cup when placing an order but fill the cup with a drink from the beverage fountain instead of filling the cup with water. The owner randomly selected 90 people who order a water cup and found that 21 of those customers filled the cup with a soft drink.a. Construct and interpret a 95 percent confidence interval for the proportion of all customers who, having asked for a water cup when placing an order, will fill the cup with a soft drink from the beverage fountain. b. The owner estimates that each customer who asks for a water cup but fills it with a soft drink costs the restaurant $0.35. Suppose that in the month of June 2,500 customers ask for a water cup when placing an order. Use the confidence interval constructed in part (a) to give an interval estimate for the cost to the restaurant for the month of June from the customers who ask for a water cup but fill the cup with a soft drink.
Answer:
This is very confusing.
Can you try and make this a shorter question for me to answer?
Step-by-step explanation:
Solve for t. t + -24 = -29 -8
what is t value?
Hope this helps
Step-by-step explanation:
t-24= -37
t= -34+24
t= -13
Answer:
t = -13
Step-by-step explanation:
Add or subtract the numbers
t- 24 = - 37t−24=−37
Separate the constants and variables
t = - 37 + 24t=−37+24
Add or subtract the numbers
t = - 13t
. Use 3.14
plss help
Answer:
A≈494.13
R = 12.54
D = 25.08
Step-by-step explanation:
Here is all the answers.
PLZZZZ give me brainliest!!!
please help guys asap
Answer:
28 i think
Step-by-step explanation:
Evaluate the following expression.
3 to power of 1
Answer:
3
Step-by-step explanation:
it is 3 3x1 is 3
Find the measure of CD in parallelogram ABCD .
Answer:
Picture would be appreciated.
Tamar surveyed six friends, asking each how many times he or she had ridden in a helicopter. The numbers of times she recorded were 0, 0, 0, 1, 3, and 8.
What is the mean absolute deviation of the number of times?
Round to the nearest tenth, if needed.
a. 0
b. 2
c. 2.3
d. 2.5
well, to do this we first need to find the mean of all values.
we need to find the distance of each value from that mean (subtract the mean from each value, ignore minus signs)
Then find the mean of those distances.
so, after we do all of that with the given numbers, our final result would be 2.333333333..... (It goes on) we round it up to 2.3, and viola! the answer is C.
Answer: the answer is c
Step-by-step explanation: i took the test
what is the volume of this composite solid
Answer:
C
Step-by-step explanation:
198 cubic meters
Scan QR code and it takes to homework so u can answer question i will give brainliest to correct answer please answer correct
im just gonna take the points for falling for that.
HELPP!! I report wrong answers!!
I need the answer for this one please
Answer:
Step-by-step explanation:
65
Find the value of −12 + 8 −(−9). Question 20 options: −13 −5 13 5
Answer:
D) 5
Step-by-step explanation:
-12 + 8 + 9 = 5
Ms. Gittens went out to dinner and the total bill was $60. She wants to give the waiter a %20 tip. How much money should Ms. Gittens give the waiter for a tip?
Answer:
$12
Step-by-step explanation:
20% of 60 = 12
Answer:
12 .....20% of 60 is = 12
Step-by-step explanation:
ramu and ravi borrowed rs 8000
Answer: Rs. 11,520
Step-by-step explanation:
As the method of compounding is not stated, the default of simple interest will be used.
Simple interest is a fixed amount that is paid over the course of the loan and is based on the original amount borrowed.
Formula is:
Amount owed = Amount borrowed * ( 1 + rate * time)
= 8,000 * ( 1 + 8% * 5.5 years)
= 8,000 * 1.44
= rs 11,520
Blake is going to invest $79,000 and leave it in an account for 9 years. Assuming the interest is compounded monthly, what interest rate, to the nearest tenth of a percent, would be required in order for Blake to end up with $96,000?
Answer:
r =2.2%
Step-by-step explanation:
Help for brainiest
please explain how you got it :D it would help so I can understand how to do the rest
Answer:
Option D
Step-by-step explanation:
Formula to use: V=[tex]\frac{1}{2}(b*a)*h\\[/tex]
b=base of triangle a=altitude of triangle h=height of prism
Doing [tex]\frac{1}{2}(b*a)[/tex] is essentially finding the area of the triangle and after multiplying by h will give you the volume of the triangular prism.
Solve: V = [tex]\frac{1}{2}(3*3)*7[/tex] or option D
Ps. Altitude is perpendicular or 90 degrees to the side I used for the base, so it wouldn't be option C.
Emma is choosing a weekly meeting time. She hopes to have two different
managers attend on a regular basis. The table shows the probabilities that
the managers can attend on the days she is proposing.
Assuming that manager A's availability is independent of manager B's
availability, which day should Emma choose to maximize the probability that
both managers will be available?
A. Monday. The probability that both managers will be available is
0.94.
B. Monday. The probability that both managers will be available is
0.67.
C. Wednesday. The probability that both managers will be available is
0.91.
D. Wednesday. The probability that both managers will be available is
0.71.
Answer:
Probability that both managers can attend:
Monday- 0.73x0.94 = 0.69
Tuesday- 0.78 x 0.91 = 0.71
So, d is correct.
Let me know if this helps!
The day Wednesday choose to maximize the probability that both managers will be available. The probability that both managers will be available is 0.71.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability can be defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
Probability that both managers can attend, consider that manager A's availability is independent of manager B's availability,
Monday;
0.73x0.94 = 0.69
Tuesday;
0.78 x 0.91 = 0.71
So, the option d is correct.
Learn more about probability here;
https://brainly.com/question/9326835
#SPJ7
What is the volume of the prism?
2 cm
3cm
11 cm PLS HURRY
Answer:
66
Step-by-step explanation:
multiply everything together
For the most recent year available, the mean annual cost to attend a private university in the United States was $50,900. Assume the distribution of annual costs follows the normal probability distribution and the standard deviation is $4,500. Ninety-five percent of all students at private universities pay less than what amount
Answer:
95% of all students at private universities pay less than $58,302.5.
Step-by-step explanation:
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.
Mean of $50,900, standard deviation of $4,500
This means that [tex]\mu = 50900, \sigma = 4500[/tex]
Ninety-five percent of all students at private universities pay less than what amount?
Pay less than the 95th percentile, and the amount is given by X when Z has a pvalue of 0.95, so X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 50900}{4500}[/tex]
[tex]X - 50900 = 1.645*4500[/tex]
[tex]X = 58302.5[/tex]
95% of all students at private universities pay less than $58,302.5.
-3/4 ( 8y - 12 ) + 1/5 ( 15y - 30 )
AY
1500-
1400
1300
Optional: How much compound
interest is earned at 35 years?
(looks to be in the middle)
compound interest
Total amount (dollars)
1200
1100
1000
900
800
700
600
500
400
300
200
100
Optional: How much simple
interest is earned at 35 years?
(looks close to the whole number)
simple interest
(a) How much more compound
interest than simple interest is
earned after 35 years?
0
5 10 15 20 25 30 35 40 45 50
Number of years
Answer:
How much compound interest is earned at 35 years? 850
How much simple interest is earned at 35 years? 600
How much more compound interest than simple interest is earned after 35 years? 250
Step-by-step explanation: