The maximum number of students that attend the trip is 160.
To determine the number of students that go on the trip, to consider the cost of theatre tickets, train tickets, and the allotted budget.
Let's denote the number of students as S. We know that the cost of each theatre ticket is £36 and that there are 2 teachers attending. Therefore, the total cost of theatre tickets for the teachers is 2 × £36 = £72.
The remaining budget after accounting for the cost of theatre tickets for the teachers is £2000 - £72 = £1928.
Each student will require a train ticket costing £12. So, the cost of train tickets for S students will be 12S.
to find the maximum number of students (S) that can be accommodated within the remaining budget.
From the remaining budget, the cost of train tickets for the students should be less than or equal to the available funds:
12S ≤ £1928
To solve for S, we divide both sides of the inequality by 12:
S ≤ £1928 / 12
S ≤ 160.67
Since the number of students must be a whole number, the maximum number of students that can go on the trip is 160.
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Find the area of an equilateral triangle (regular 3-gon) with the given measurement: 6-inch radius. A = sq. in.
The correct answer is 27√3
Answer: The area or "the answer" will be 27√3
Step-by-step explanation:
austin swam 1.4 laps each minute. Ashley is Austin's older sister. she trains in the same pool and can swim 9 laps in 6 minutes. is ashley a faster swimmer than Austain?
Answer:
Since Ashley swam more laps per minute, she's a faster swimmer than Austin.
Step-by-step explanation:
Austin:
She swam 1.4 laps per minute
Ashley:
9 laps in 6 minutes
So, per minute
9/6 = 1.5 laps per minute
Since Ashley swam more laps per minute, she's a faster swimmer than Austin.
Answer:
t
Step-by-step explanation:
10/9 = 3/q
solve for q
Answer:
Q= 27/10
Step-by-step explanation:
Answer: [tex]q=\frac{27}{10}[/tex]
Step-by-step explanation:
[tex]\frac{10}{9}=\frac{3}{q}[/tex]
Multiply by q.
[tex]q*\frac{10}{9}=\frac{3}{q}*q[/tex]
[tex]\frac{10}{9}q=3[/tex]
Now multiply by the reciprocal of [tex]\frac{10}{9}[/tex] which is the inverted fraction. [tex]\frac{9}{10}[/tex]
[tex]\frac{9}{10}*\frac{10}{9}q=3*\frac{9}{10}[/tex]
[tex]q=\frac{27}{10}[/tex]
6. Construct Arguments Gia researches online
that her car is worth $3,000. She hopes to sell
it for 85% of that value, but she wants to get
at least 70%. She ends up selling it for $1,800
Did she get what she wanted? Justify your
answer.
Answer:
noGia sold it for 60% of its valueStep-by-step explanation:
The amount Gia got for her car was ...
1800/3000 × 100% = 60%
of the amount it is worth. This percentage is less than the 70% Gia wanted as a minimum. She did not get what she wanted.
a high school graduating class is made up of 351 students. There a 73 more girls than boys. How many boys are in the class
Answer:
139 boys
Step-by-step explanation:
Using the given information, we can set up a system of equations.
Let the number of girls in the class be x and let the number of boys in the class be y.
x + y = 351
x = y + 73
Solving this system of equations would tell you that there are 139 boys in this graduating class.
Leave a comment if you want me to be a bit more in-depth.
The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 31 minutes of calls is $21.28, and the remaining credit after 69 minutes of calls is $16.72. What is the remaining credit after 76 minutes of calls?
Answer:
$15.88
Step-by-step explanation:
[tex]\frac{(21.28 - 16.72)}{(69-31)}[/tex]
$4.56 / 38 min
$0.12 / 1 min
76 - 69 = 7 minutes
7 x .12 = .84
16.72 - .84 = 15.88
find the zero of picture is included
Answer:
x = -12/6 = -2
x = -18/6 = -3
Step-by-step explanation:
The zeros in an equation is the same thing as the x's.
3x²+15x+18 = 0 (Where a = 3, b = 15, c = 18)
One thing you could do to find the answer is use the quadratic formula:
x = (-b ± √(b²-4ac))/2a =
(-15 ± √15² - (4*3*18))/2*3 =
(-15 ± √225 - 216)/6 =
(-15 ± √9)/6 =
(-15 ± 3) / 6.
To find the first x we need to do (-15 + 3) / 6 and to find the second x we need to do (-15-3) / 6.
x = -12/6 = -2
x = -18/6 = -3
To find the zeros of the quadratic equation 3x^2 + 15x + 18 = 0, use the quadratic formula to obtain the values of x.
To find the zeros of the quadratic equation 3x^2 + 15x + 18 = 0, we can use the quadratic formula.
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Plugging in the values from our equation, we get:
x = (-15 ± sqrt(15^2 - 4*3*18)) / (2*3)
After evaluating the expression, we find that the zeros of the equation are x = -3 and x = -2.
The probable question may be:
find the zero of 3x^2+15x+18=0 using any method.
Find the sum of 526+213 by breaking apart the addenda into hundreds
Solve (x - 5)^2 = 3
Answer:
c
Step-by-step explanation:
√(x-5)²=±√3
x-5=±√3
x=5±√3
To solve the quadratic equation (x - 5)² = 3, take the square root of both sides to give x - 5 = ± √3, then add 5 to each side to give x = 5 ± √3. The two possible solutions are x = 5 + √3 and x = 5 - √3.
Explanation:The question is asking to solve the equation (x - 5)² = 3. This is a quadratic equation in the form (x-a)² = b. To solve it, you should start by taking the square root on both sides.
Step 1: √[(x - 5)²] = √[3]
This leads to: x - 5 = ± √3
Step 2: Followed by adding 5 to both sides
x = 5 ± √3
So there are two possible solutions: x = 5 + √3 and x = 5 - √3.
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find the value of p+7 when p=19
Answer:
26
Step-by-step explanation:
p = 19
p + 7 = 19 + 7
= 26
So, the value of p + 7 is 26
Hope it helps and is useful :)
The function 3(2)t models the number of leaves on a plant, where t represents the number of weeks since it was planted. Which statement is the best interpretation of one of the values in this function? A) The number of leaves increases by 6 each week. B) The initial number of leaves on the plant was 2. C) The initial number of leaves on the plant was 3. D) The number of leaves on the plant increases by 3% each week.
Answer:
C) The initial number of leaves on the plant was 3.
Step-by-step explanation:
The plant has initially 3 leaves and is multiplied by 2 every week. Therefore, the answer is C.
The slope of a pipe with a 1/4 inch of drop has a run of 1 foot. What is the run of a pipe that has a 3/4 inch drop?
Answer: 3 foot
Step-by-step explanation:
Which figure cannot be made by slicing through a cube? Select all that apply.
A
a circle
B
an octagon
C
a rectangle
D
a square
E
a decagon
F
a triangle
Answer:
A. a circle, B. an octagon, E. a decagon, F. a triangle
Step-by-step explanation:
Squares and rectangles can be made by slicing a cube.
Answer:
A
a circle
B
an octagon
E
a decagon
Step-by-step explanation:
I had this question on my math test and these are correct
Which theorem proves that angle EHF = Angle EGF?
A. The measure of an inscribed angle is half the measure of its intercepted arc.
B. Two inscribed angles that intercept the same arc are congruent.
C. An angle inscribed in a semicircle is a right angle.
D. The opposite angles of a quadrilateral inscribed in a circle are supplementary
Answer:B) Two inscribed angles that intercept the same arc are congruent.
Step-by-step explanation:
I just took the test
Email marketing, the online counterpart of direct mail marketing, can be a highly personalized, very targeted means of communication. With its very low cost and wide reach, you feel that email marketing must play a major role in Caffè Gustoso's online advertising campaign.
The owners want to send as many emails as possible to potential customers. However before you send out the first email, you have to choose an email permission strategy.
Select an option from the choices below:
a. Opt-in: Request the consumer's permission before sending any Caffé Gustoso email correspondence.
b. Unsolicited: Send unsolicited Caffe Gustoso email to a large number of potential customer.
c. Opt-out: Allow consumers to quest to be removed from have been contacted
Answer:
c. Opt-out: Allow consumers to quest to be removed from have been contacted.
Step-by-step explanation:
The Caffe Gutoso is considering a marketing strategy to promote its business. The owner want to send emails to its potential customers. Before sending the email the sender must insert email permission strategy as send an email from Caffe Gutoso and place and Opt-out option for those customers who are not willing to receive any email from the Caffe.
complete the table for the given rule y=x-1/4
Answer:
Is there a picture of the table I will try and solve but I'm not sure if I can
Answer:
0,3,7/4
Step-by-step explanation: In the equation,x-1/4 means 1/4 is subtracted from x to find each value of y,we need to take each value of x and subtract 1/4 for example: when x = 1/4: y = 1/4 - 1/4 , y = 0
Calculate the lower quartile of the data set for the blood glucose levels of 10 individuals whose blood glucose readings were as follows: 88, 97, 101, 104, 104, 107, 109, 117, 121, and 147
Final answer:
To find the lower quartile of a data set, sort the data in ascending order and find the median of the lower half.
Explanation:
To calculate the lower quartile of a data set, you need to find the median of the lower half of the data. In this case, we have 10 blood glucose readings. To find the lower quartile:
First, sort the data in ascending order: 88, 97, 101, 104, 104, 107, 109, 117, 121, 147.
Since we have an even number of values (10), the lower half has 10/2 = 5 values.
The median of the lower half of the data is the average of the two middle values: 104 and 104. So, the lower quartile is 104.
To get an estimate of consumer spending over a holiday season in 2009, 436 randomly sampled American adults were surveyed. Their spending for the six-day period after Thanksgiving, spanning the Black Friday weekend and Cyber Monday, averaged $84.71. A 95% confidence interval based on this sample is ($80.31, $89.11). Which of the following statements are true? Select all that apply. A 90% confidence interval would be narrower than the 95% confidence interval if we don't need to be as sure about our estimate. In order to decrease the margin of error of a 95% confidence interval to a third of what is is now, we would need to use a sample 3 times larger. This confidence interval is not valid since the distribution of spending in the sample data is right skewed. The margin of error is $4.4. We are 95% confident that the average spending of these 435 American adults over this holiday season is between $80.31 and $89.11. This confidence interval is valid since the sampling distribution of sample mean would be approximately normal with sample size of 436. 95% of random samples have a sample mean between $80.31 and $89.11. We are 95% confident that the average spending of all American adults over this holiday season is between $80.31 and $89.11.
Answer:
-A 90% confidence interval would be narrower than the 95% confidence interval if we don't need to be as sure about our estimate.
-This confidence interval is not valid since the distribution of spending in the sample data is right skewed.
-The margin of error is $4.4.
-This confidence interval is valid since the sampling distribution of sample mean would be approximately normal with sample size of 436.
-We are 95% confident that the average spending of all American adults over this holiday season is between $80.31 and $89.11.
Step-by-step explanation:
A 90% confidence interval would be narrower than the 95% confidence interval if we don't need to be as sure about our estimate.
TRUE. The 90% confidence is less strict in its probability of having the mean within the interval, so it is narrower than the 95% CI. It relies more in the information given by the sample.
In order to decrease the margin of error of a 95% confidence interval to a third of what is is now, we would need to use a sample 3 times larger.
FALSE. The margin of error is z*σ/(n^0.5). So to reduce it by two thirds, the sample size n needs to be 3^2=9 times larger.
This confidence interval is not valid since the distribution of spending in the sample data is right skewed.
FALSE. There is no information about the skewness in the sample.
The margin of error is $4.4.
TRUE. The margin of error is (89.11-80.31)/2=$4.4.
We are 95% confident that the average spending of these 435 American adults over this holiday season is between $80.31 and $89.11.
FALSE. The CI is related to the populations mean. We are 95% confident that the average spending of the population is between $80.31 and $89.11.
This confidence interval is valid since the sampling distribution of sample mean would be approximately normal with sample size of 436.
TRUE. This happens accordingly to the Central Limit Theorem.
95% of random samples have a sample mean between $80.31 and $89.11.
FALSE. The confidence interval refers to the population mean.
We are 95% confident that the average spending of all American adults over this holiday season is between $80.31 and $89.11.
TRUE. This is the conclusion that is looked for when constructing a confidence interval.
Two bottling plants package a certain type of sports drink. Suppose the mean volume of all of this type of sports drinks is 20 fluid ounces. Bottling plant A bottles an average of 50,000 sports drinks per day. Bottling plant B bottles an average of 175,000 sports drinks per day. On a particular day, which bottling plant is less likely to record a mean volume of 21 fluid ounces for the day?
Answer:
Bottling plant B (with 175,000 sports drinks per day), because the daily mean will be closer to 21 fluid ounces with more sports drinks in the sample.
Given Information:
Mean volume = μ = 20 fl oz
Sampling size of plant A = n₁ = 50,000 drinks/day
Sampling size of plant B = n₂ = 175,000 drinks/day
Required Information:
Which bottling plant is less likely to record a mean volume of 21 fl oz ?
Answer:
Plant B is less likely to record a mean volume of 21 fl oz
Step-by-step explanation:
The standard deviation of the plant A is given by
σa = σ/√n₁
The standard deviation of the plant B is given by
σb = σ/√n₂
Where σ is standard deviation for the mean volume of 20 fl oz and it is fixed.
As you can notice in the above relation, the standard deviation of the plants depend upon the number of samples (n). As the number of sample increases, the standard deviation of samples decreases which means that the mean of the samples will be closer to the actual mean (that is 20 fl oz).
Since the plant B has more samples (n₂ = 175,000) then its standard deviation (σb) will be less and the mean will be closer to 20 fl oz therefore, it is less likely that it will record a mean of 21 fl oz.
Plant A is more likely to record a mean volume of 21 fl oz
Mr. Gordon has 13 girls and 14 boys in his fourth period algebra class. One person is chosen at random.
What is the probability that the person chosen is a boy?
A. 1/14
B. 1/27
C. 13/14
D. 13/27
E. 14/27
Answer:
E
Step-by-step explanation:
It's E because you have to add 13 and 14 and as you can see there's 14 boys so it's E.
The probability that the person chosen is a boy is 14/27.
Number of girls = 13
Number of boys = 14
Total students = 27
What is probability?Probability is a measure of the likelihood of occurrence of an event.
P(event) = Favorable outcomes / total outcomes
Favourable outcomes = 14 because there are 14 boys
Total outcomes =27
So, the probability that the person chosen is a boy will be given by:
P(boy)=14/27
So, the probability that the person chosen is a boy is 14/27.
Hence, the probability that the person chosen is a boy is 14/27.
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What is the answer?
A. Infinite Number of Solutions
B. (3, 3)
C. (3, -3)
D. (-3, 3)
Answer:
It's either B or A
Step-by-step explanation:
If I had to choose one I would pick B because I did the math; and logically, that answer makes the most sense.
A baseball is hit, and rises to a height above the ground, f(t), in feet, at time t, in seconds, can be estimated by the formula: f(t)=-10t^(2)+40t+8
Answer:
The maximum height reached by the baseball is 48 feet.Step-by-step explanation:
The given function is
[tex]f(t)=-10t^{2}+40t+8[/tex]
To find the maximum height reached by the ball, we need to find the vertex of the parabolla represented by the given quadratic equation.
Remember that a vertex has coordinates (h,k), where [tex]h=-\frac{b}{2a}[/tex] and [tex]k=f(h)[/tex].
According to the given function, we have
[tex]a=-10[/tex] and [tex]b=40[/tex]
[tex]h=-\frac{40}{2(-10)}=\frac{40}{20}=2[/tex]
[tex]k=f(2)=-10(2)^{2} +40(2)+8=-10(4)+80+8=-40+80+8=48[/tex]
So, the vertex has coordinates of (2,48), which means the maximum height reached by the baseball is 48 feet.
The typical lifespan for various mammal species in captivity (L) in years has been related to averageadult size (M) in kilograms according to the regression equation seen below. A typical adult Meerkat weighs about 0.9 kilograms. What is the predicted lifespan of a Meerkat incaptivity, according to this equation? * 2 points 11.6 years 2.4 years 14.1 years 2.6 years 28.8 years
Complete Question:
The typical lifespan for various mammal species in captivity (L) in years has been related to average adult size (M) in kilograms according to the regression equation seen below.
[tex]ln L = 2.468 + 0.2 (lnM)[/tex]
A typical adult Meerkat weighs about 0.9 kilograms. What is the predicted lifespan of a Meerkat incaptivity, according to this equation? * 2 points 11.6 years 2.4 years 14.1 years 2.6 years 28.8 years
Answer:
Option A) L = 11.6 years
Step-by-step explanation:
From the given equation:
[tex]ln L = 2.468 + 0.2 (lnM)[/tex]..........(1)
Average adult size, M = 0.9 kg
Putting the value of M into the regression equation in (1)
[tex]ln L = 2.468 + 0.2 (ln0.9)\\ln L = 2.468 + (-0.02107)\\ln L = 2.447\\L = e^{2.447} \\L = 11.55 years[/tex]
The question is an illustration of regressions.
The lifespan of a typical adult Meerkat that weighs about 0.9 kilograms is (a) 11.6 years
The regression equation is given as:
[tex]\ln(L) = 2.468 + 0.2\ln(M)[/tex]
From the question, we have:
M = 0.9
Substitute 0.9 for M in [tex]\ln(L) = 2.468 + 0.2\ln(M)[/tex]
[tex]\ln(L) = 2.468 + 0.2\ln(0.9)[/tex]
Take natural logarithm of 0.9
[tex]\ln(L) = 2.468 + 0.2\times -0.1054[/tex]
[tex]\ln(L) = 2.468 -0.02108[/tex]
[tex]\ln(L) = 2.44692[/tex]
Take exponents of both sides
[tex]L = e^{2.44692}[/tex]
[tex]L = 11.553[/tex]
Approximate
[tex]L = 11.6[/tex]
Hence, the lifespan is (a) 11.6 years
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Suppose the round-trip airfare between Boston and Orlando follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50. What is the probability that a randomly selected airfare between Boston and San Francisco will be less than $300
The probability that a randomly selected airfare between Boston and Orlando will be less than $300 is approximately 10.04%.
To find the probability that a randomly selected airfare between Boston and Orlando will be less than $300, we need to calculate the z-score and use the standard normal distribution table.
Calculate the z-score: z = (x - mean) / standard deviation = (300 - 387.20) / 68.50 = -1.2768. Look up the corresponding z-score in the standard normal distribution table. The area to the left of z = -1.28 is 0.10035.Therefore, the probability that a randomly selected airfare between Boston and Orlando will be less than $300 is approximately 0.10035, or 10.04%.
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Problem 8-4 A computer time-sharing system receives teleport inquiries at an average rate of .1 per millisecond. Find the probabilities that the number of inquiries in a particular 50-millisecond stretch will be:
Answer: a) 0.9980, b) 0.0013, c) 0.0020, d) 0.00000026, e) 0.0318
Step-by-step explanation:
Problem 8-4 A computer time-sharing system receives teleport inquiries at an average rate of .1 per millisecond. Find the probabilities that the number of inquiries in a particular 50-millisecond stretch will be:
Since we have given that
[tex]\lambda=0.1\ per\ millisecond=5\ per\ 50\ millisecond=5[/tex]
Using the poisson process, we get that
(a) less than or equal to 12
probability= [tex]P(X\leq 12)=\sum _{k=0}^{12}\dfrac{e^{-5}(-5)^k}{k!}=0.9980[/tex]
(b) equal to 13
probability= [tex]P(X=13)=\dfrac{e^{-5}(-5)^{13}}{13!}=0.0013[/tex]
(c) greater than 12
probability= [tex]P(X>12)=\sum _{k=13}^{50}\dfrac{e^{-5}.(-5)^k}{k!}=0.0020[/tex]
(d) equal to 20
probability= [tex]P(X=20)=\dfrac{e^{-5}(-5)^{20}}{20!}=0.00000026[/tex]
(e) between 10 and 15, inclusively
probability=[tex]P(10\leq X\leq 15)=\sum _{k=10}^{15}\dfrac{e^{-5}(-5)^k}{k!}=0.0318[/tex]
Hence, a) 0.9980, b) 0.0013, c) 0.0020, d) 0.00000026, e) 0.0318
Using the Poisson distribution, the probability of x inquires in a particular 50-millisecond stretch will be:
[tex]P(X = x) = \frac{e^{-5}5^{x}}{(x)!}[/tex]
In this problem, we are given the mean during an interval, which means that the Poisson distribution is used.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successes
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given interval.
We are given an average rate of 0.1 inquires per millisecond.
50-millisecond interval, thus [tex]\mu = 50(0.1) = 5[/tex]
Then, the probability of x inquires in a particular 50-millisecond stretch will be:
[tex]P(X = x) = \frac{e^{-5}5^{x}}{(x)!}[/tex]
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In a chess tournament, each player plays every other player exactly once. If it is known that 105 games were played, how many players were there in the tournament?
Answer:
15 players played in the chess tournament.
Step-by-step explanation:
When there are 15 players, the first player plays 14 games and step aside.
remaining 14 player
next player plays 13 games. steps aside
remaining 13 players
next player plays 12 games. steps aside
remaining 12 players
next player plays 11 games. steps aside
remaining 11 players
.
.
.
.
Last player plays 1 game and steps aside
remaining 1 player who will not play against himself.
∴ Sum of all games played
= 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 105 games played
Answer:
Step-by-step explanation:
Let be the number of players. There was a game for every pair of players, so there must be 105 pairs of players.
(−1)/2=105.
should be easy to solve after that.
A particular fruit's weights are normally distributed, with a mean of 426 grams and a standard deviation of 37 grams. If you pick 9 fruit at random, what is the probability that their mean weight will be between 413 grams and 464 grams. Round to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 2 decimal places are accepted.
Answer:
Probability that their mean weight will be between 413 grams and 464 grams is 0.8521.
Step-by-step explanation:
We are given that a particular fruit's weights are normally distributed, with a mean of 426 grams and a standard deviation of 37 grams.
Also, you pick 9 fruit at random.
Let [tex]\bar X[/tex] = sample mean weight
The z-score probability distribution for sample mean is given by;
Z = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean weight = 426 grams
[tex]\sigma[/tex] = population standard deviation = 37 grams
n = sample of fruits = 9
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.
So, probability that the mean weight of 9 fruits picked at random will be between 413 grams and 464 grams is given by = P(413 grams < [tex]\bar X[/tex] < 464 grams) = P([tex]\bar X[/tex] < 464 grams) - P([tex]\bar X[/tex] [tex]\leq[/tex] 413 grams)
P([tex]\bar X[/tex] < 464 grams) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{464-426}{\frac{37}{\sqrt{9} } }[/tex] ) = P(Z < 3.08) = 0.99896
P([tex]\bar X[/tex] [tex]\leq[/tex] 413 grams) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{413-426}{\frac{37}{\sqrt{9} } }[/tex] ) = P(Z [tex]\leq[/tex] -1.05) = 1 - P(Z < 1.05)
= 1 - 0.85314 = 0.14686
{Now, in the z table the P(Z [tex]\leq[/tex] x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 3.08 and x = 1.05 in the z table which has an area of 0.99896 and 0.85314 respectively.}
Therefore, P(413 grams < [tex]\bar X[/tex] < 464 grams) = 0.99896 - 0.14686 = 0.8521
Hence, the probability that their mean weight will be between 413 grams and 464 grams is 0.8521.
The life in hours of a biomedical device under development in the laboratory is known to be approximately normally distributed. A random sample of 15 devices is selected and found to have an average life of 5311.4 hours and a sample standard deviation of 220.7 hours.
a. Test the hypothesis that the true mean life of a biomedical device is greater than 500 using the P-value approach.
b. Construct a 95% lower confidence bound on the mean.
c. Use the confidence bound found in part (b) to test the hypothesis.
Answer:
a)Null hypothesis:- H₀: μ> 500
Alternative hypothesis:-H₁ : μ< 500
b) (5211.05 , 5411.7)
95% lower confidence bound on the mean.
c) The test of hypothesis t = 5.826 >1.761 From 't' distribution table at 14 degrees of freedom at 95% level of significance.
Step-by-step explanation:
Step :-1
Given a random sample of 15 devices is selected in the laboratory.
size of the small sample 'n' = 15
An average life of 5311.4 hours and a sample standard deviation of 220.7 hours.
Average of sample mean (x⁻) = 5311.4 hours
sample standard deviation (S) = 220.7 hours.
Step :- 2
a) Null hypothesis:- H₀: μ> 500
Alternative hypothesis:-H₁ : μ< 500
Level of significance :- α = 0.95 or 0.05
b) The test statistic
[tex]t = \frac{x^{-} - mean}{\frac{S}{\sqrt{n-1} } }[/tex]
[tex]t = \frac{5311.4 - 500}{\frac{220.7}{\sqrt{15-1} } }[/tex]
t = 5.826
The degrees of freedom γ= n-1 = 15-1 =14
tabulated value t =1.761 From 't' distribution table at 14 degrees of freedom at 95% level of significance.
calculated value t = 5.826 >1.761 From 't' distribution table at 14 degrees of freedom at 95% level of significance.
Null hypothesis is rejected at 95% confidence on the mean.
C) The 95% of confidence limits
[tex](x^{-} - t_{0.05} \frac{S}{\sqrt{n} } ,x^{-} + t_{0.05}\frac{S}{\sqrt{n} } )[/tex]
substitute values and simplification , we get
[tex](5311.4 - 1.761 \frac{220.7}{\sqrt{15} } ,5311.4 +1.761\frac{220.7}{\sqrt{15} } )[/tex]
(5211.05 , 5411.7)
95% lower confidence bound on the mean.
What is the value and is it minimum or max
Answer:
minimum and value of 4
Step-by-step explanation:
[tex]\frac{dx}{dy} = 2x-8[/tex]
When [tex]\frac{dx}{dy}=0[/tex] we will be able to get the critical points.
[tex]2x-8 =0[/tex][tex]x=4[/tex]
The graph is a quadratic graph with a 'U' shape, thus it has a minimum critical point.
Two baseball players bat first and second in the lineup. The first batter has an on-base percentage of 0.23. The second batter has an on-percentage of 0.38 if someone is on base, but only 0.26 if the bases are empty. At the start of the game, what is the probability that neither player gets on base?
Answer:
The probability that neither player gets on base is 0.4824
Step-by-step explanation:
1. Both players get to base. Just multiply the two probabilities together:
= (probability first batter gets on base) x (probability second batter gets on base, if the first batter gets on base)
= 0.23 x 0.38
= 0.0874
2. One player gets to base. The formula here is P(A+B) =P(A) + P(B) - P(A) x P(B)
= (probability first batter gets on base) + (probability second batter gets on base, if the first batter does not) - (0.23 x 0.26)
= 0.23 + 0.26 - (0.23 x 0.26)
= 0.49 - 0.0598
= 0.4302
3. Neither player gets to base = 1 - addition of the previous two cases.
= 1 - (0.0874 + 0.4302)
= 1 - 0.5176
= 0.4824