Answer:
0.9544 = 95.44% probability that a new sample this year of 100 steady smokers spends between $19 and $21 on average
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 firm found that the population mean amount that all smokers spend on cigarettes is $20 and the population standard deviation is $5.
This means that [tex]\mu = 20, \sigma = 5[/tex]
Sample of 100:
This means that [tex]n = 100, s = \frac{5}{\sqrt{100}} = 0.5[/tex]
What is the probability that a new sample this year of 100 steady smokers spends between $19 and $21 on average?
This is the pvalue of Z when X = 21 subtracted by the pvalue of Z when X = 19. So
X = 21
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{21 - 20}{0.5}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
X = 19
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{19 - 20}{0.5}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a pvalue of 0.0228
0.9772 - 0.0228 = 0.9544
0.9544 = 95.44% probability that a new sample this year of 100 steady smokers spends between $19 and $21 on average
The graph of a line and and exponential intersect twice, once, or not at all. Describe the possible number of intersections of each of the following pairs of graph. Your solution to each part should include all of the possibilities and a quickly sketched example of each one. (Part 1)(SHOW WORK)
a. A line and a parabola
b. Two different parabolas
a) A line can intersect a parabola at 2 points, 1 point, or no points respectively. The only possible way at which it intersects at 1 point, would be if it were tangent to the parabola. [Check first attachment]
b) Two different parabolas can intersect at 2 points, 1 point or no points respectively. [Check second attachment]
It is possible for 2 parabolas to intersect at 4 and even 3 points. But one of the parabolas would be on it's side. You can consider those cases.
Guys!!! Please help!! Geesh I need help
Answer:
42
Step-by-step explanation:
9 - 4 = 5
8 - 5 = 3
9 + 2 + 3 + 7 + 8 + 3 + 4 + 6 = 42
Answer:
Its 42 ;l
Step-by-step explanation:
A catering company charges a flat fee of 120$ to cater an event...
Keisha is babysitting at $8 per hour to earn money for a car. So far she has saved $1300. The car that Keisha wants to buy costs at least $5440. Write and solve an inequality to determine the amount Keisha still needs to earn for the car.
Answer:
$4100
Step-by-step explanation:
For Kaisha to get this car we have these information available
Amount saved = $1300
The cost of the car = $5400
Let The amount left to complete the car = k
We have this equation
K + $1300 = $5400
K = 5400 - 1300
K = 4100
Therefore Kaisha still needs to earn an additional amount of $4100 for the total amount of the car to be completed.
what is the solution to the system of equations?
3x - 6y = -12
2x - 4y = -16
please help!!
For the following studies in which tests comparing two means are conducted, select whether the populations are independent or matched pairs:
a. A study is conducted to see what effect a new drug has on dexterity. A random sample of 30 people is chosen. They are given a series of tasks to perform and a score reflecting their performance. A dose of the drug is administered to the 30 people, and they are then given a similar series of tasks to perform and scored again.
b. A study is conducted to determine the difference between the average amount that people spend on durables and non-durables when they go shopping. A sample of people is chosen and their shopping purchases are observed.
c. A study is conducted to determine if there is a difference between the average length of time spent in traffic on the way to work and the average length of time spent in traffic going home from work for people in a city. A random sample of workers is chosen and asked how long they spend getting to work. Another separate random sample of workers is chosen and asked how long they spend getting home from work.
Answer:
a. Independent
b. Matched
c. Independent
Step-by-step explanation:
If the sample is chosen randomly and there is no biasness in the selection of sample from the population then the selected sample is independent. The matched pairs are when the selection process involves a relation with the sample selected with the desired test results.
We can conclude that:
a. the population is independent.
b. the population is matched.
c. the population is independent.
What are Independent and Matched Populations?If a researcher selects a sample from an entire population under study in a random and unbiased manner, the sample population is aid to be independent.
If the selection process in drawing the sample involves a relation with what is expected from the test results, then they are is matched pairs.
Thus, we can conclude that:
a. the population is independent.
b. the population is matched.
c. the population is independent.
Learn more about independent and matched populations on:
https://brainly.com/question/17143411
WORTH 35 POINTS!!! Annie’s dad travels for business. On Monday, he drives for 4 hr. at a constant rate of 55 mph to meet with a customer. On Tuesday, he drives 3 hr. at a constant rate of 50 mph to meet with his district sales manager. On Wednesday, he drives 2 hr. at a constant rate of 60 mph to pick up supplies at the warehouse. How many miles does Annie’s dad drive total before he heads for home?
A. 120 mi.
B. 150 mi.
C. 220 mi.
D. 490 mi.
Answer:
220mi
Step-by-step explanation:
Annie's dad drove a total of 490 miles before heading home. The correct option is D.
What is the distance?Distance is defined as the product of speed and time.
We can use the formula distance = rate x time to calculate the distance for each day.
On Monday, he drove for 4 hours at 55 mph, so the distance he traveled was:
distance = 55 mph x 4 hours = 220 miles
On Tuesday, he drove for 3 hours at 50 mph, so the distance he traveled was:
distance = 50 mph x 3 hours = 150 miles
On Wednesday, he drove for 2 hours at 60 mph, so the distance he traveled was:
distance = 60 mph x 2 hours = 120 miles
To find the total distance, we can add up the distances for each day:
220 miles + 150 miles + 120 miles = 490 miles
Therefore, Annie's dad drove a total of 490 miles before heading home.
Learn more about distance here:
brainly.com/question/13269893
#SPJ3
I don’t know what to do
Answer:
okay so, everytime you see anything that says "a number", that will automatically mean that there is a number in the equation that u dont know, so instead of putting a random number in its place, you put an "exponent" aka a letter like "x" for example. so it says, 12 is the sum of a "number" and 3, that means 3 plus a number gives u 12, you would have to make an equation to find the "number" so the equation would be "3 + x = 12".
Step-by-step explanation:
Which answer best describes the shape of this distribution? skewed left skewed right uniform bell-shaped
Answer:
Skewed right
Step-by-step explanation:
Most of the data is to the right, so it's not skewed left.
Uniform is mostly even, so not that either.
Bell shape is centered and vaguely triangular, so incorrect, hence the only remaining option is skewed right.
Hope this helps :)
Stay Cold,
Brook
I need help with this problem please.
Step-by-step explanation:
Airplane One 425m/h x 2h= 850 miles traveled N5°W
Airplane Two 530m/h x 2h= 1060 miles traveled N67°E
5 degrees + 67 degrees = 72 degrees divergence of the Airplane One and Two
Draw a triangle, the smallest side is 850 and adjacent to 1060 side. The angle between these two sides is 72 degrees
Use the acronym SOH CAH TOA to find the side which is the distance between the 2 airplanes after 2 hours
sine 72= opposite/hypotheneus
sine 72= opposite/1060
opposite = (sine 72)(1060)= 1008 miles distance between Airplane One and Airplane Two
Can someone provide some assistance.
Answer:
m<E=120°
m<T=60°
Step-by-step explanation:
10m+4m+12=180
14m=168
m=12
m<E=10m=10(12)=120
m<T=4m+12=4(12)+12=48+12=60
Answer:
Solution given:
10m+4m+12=180°[sum of opposite angle of cyclic quadrilateral is supplementary]
14m=180-12
m=168/14=12
m<E=10×12=120°
m<T=4×12+12=60°
plz help asap!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
a 12/20 = 0.6
b 21/35 = 0.6
c 28.8/48 = 0.6
Use the Distributive Property to
REWRITE 5(p - 8)
Sam opened a saving account with a deposit and then started saving the same amount each
month. After 3 months Sam had $325 in he account. After 7 months she had $625 in her
account. Write an equation for this situation.
Amelia earned $100 on a $1000 investment with a bank for a 3-year term. what rate did the bank offer her?
Answer:
3.33%
Step-by-step explanation:
Rate = 100xSI / PxT
P = 1000
SI = 100
T = 3
Rate = 100 x 100 / 1000 x 3 = 3.33%
Ashley and Emma are reading the same article. Ashley is on page 1 of the article, but she can read 1 page per minute. Emma is already on page 5, but reads a page every 3 minutes.
What page is Ashley on after 5 minutes.
What equation can be used to represent the amount Emma has read?
How many minutes does it take before Ashley and Emma have read the same amount
Answer:
Part A)
Ashley will be on the sixth page.
Part B)
[tex]\displaystyle p=\frac{1}{3}m+5[/tex]
Part C)
Six minutes.
Step-by-step explanation:
Ashley is on the first page and she can read one page per minute.
Emma is on the fifth page and she can read one page every three minutes.
Part A)
We can write an equation for Ashley. Let m represent the amount of minutes that has passed.
Since she is already one the first page, our initial value is 1.
She reads one page every minute. So, after m minutes, she would have read m pages.
Therefore, our equation is:
[tex]p=m+1[/tex]
Where p is the total pages read after m minutes.
Then after five minutes, Ashley will be on the:
[tex]p=(5)+1=6[/tex]
Ashley will be on the sixth page after five minutes.
Part B)
Since Emma reads one page every three minutes, we can say that she reads 1/3 of a page every minute.
Since she started on page five, her equation is:
[tex]\displaystyle p=\frac{1}{3}m+5[/tex]
Part C)
So, both of their pages read must be equivalent. Therefore:
[tex]\displaystyle m+1=\frac{1}{3}m+5[/tex]
Solve for m. Subtract 1/3m from both sides:
[tex]\displaystyle \frac{2}{3}m+1=5[/tex]
Subtract 1 from both sides:
[tex]\displaystyle \frac{2}{3}m=4[/tex]
Finally, multiply both sides by 3/2:
[tex]\displaystyle m=4\Big(\frac{3}{2}\Big)=6[/tex]
So, it will take six minutes before Ashley and Emma have read the same number of pages.
7 ft equals blank inches
Answer:
it is 84 inches all together
Answer:
84 inches
Step-by-step explanation:
have a good day
may i please get a branlillest
Which number line represents the solution of 5X < 30
Answer:
Step-by-step explanation:
Answer:
BRO, where are the number lines, can't help you if you dont put the number lines
Please help with this question. This is due today!
Answer:
3x° = 60°
2x° = 40°
Step-by-step explanation:
3x + 80 +2x = 180° (Linear Pair)
5x + 80 = 180
5x = 180 - 80
5x = 100
x = 20
Substituting the value for x,
3x° = 3 × 20 = 60°
2x° = 2 × 20 = 40°
−4.5=−0.5(x−7.1)
solve for x and teach me how to give brainliest
help with math please it means the world to me!!
Answer:
10 units^2
Step-by-step explanation:
How many negative real zeros does f(x) = x^5 - 2x^4 - 4x^3 + 4x2 – 5x + 6 have?
A. 3
B. 2
C. 1
D. 0
sarah has 3 dozen eggs. she sold 3/4 of her eggs, how many eggs did she sell?
Answer:
27
Step-by-step explanation:
Which statement about the ordered pair (-6,8) is true?
Answer:
a
Step-by-step explanation:
solve for y in one equation
2x + y = -4
y = -4 - 2x
plug y into the other equation
5x + 3y = -6
5x + 3(-4 - 2x) = -6
5x -12 -6x = -6
-x - 12 = -6
-x = 6
x = -6
plug x into the equation to find y
y = -4 - 2x
y = -4 - 2(-6)
y = 8
ordered pair: (-6,8)
Identify all the acute angles in the figure.
Please help me I tired of keep asking. If you have a heart you would help me and give me the right answer Please (NO LINKS) (NO LYING )
Answer:quit
Step-by-step explanation:that looks lard
I need help please help
Please answer this correctly without making mistakes I want ace expert and genius people to answer this correctly without making mistakes
Answer:
Step-by-step explanation:
(h+2)+9
b-(6-4)
What is $6.977 rounded to the nearest cent
Answer:
6.98
Step-by-step explanation:
You just round the seven up
Tess works at a sandwich shop. When assembling their turkey sandwich, they are instructed to use 5 pieces of sliced turkey and 2 pieces of cheese. If Tess is assembling a party platter of these turkey sandwiches and uses 12 pieces of cheese, how many slices of turkey will she use?