Answer:
1. 0.7421 = 74.21% probability the elevator is overloaded.
2. D.No, there is a good chance that 10 randomly selected people will exceed the elevator capacity.
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 establishes 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.
Assume that weights of males are normally distributed with a mean of 166 lb and a standard deviation of 29 lb.
This means that [tex]\mu = 166, \sigma = 29[/tex]
Sample of 10.
This means that [tex]n = 10, s = \frac{29}{\sqrt{10}}[/tex]
1.The probability the elevator is overloaded is?
Probability that the sample mean is above 160 pounds, which is 1 subtracted by the p-value of Z when X = 160. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{160 - 166}{\frac{29}{\sqrt{10}}}[/tex]
[tex]Z = -0.65[/tex]
[tex]Z = -0.65[/tex] has a p-value of 0.2579.
1 - 0.2579 = 0.7421
0.7421 = 74.21% probability the elevator is overloaded.
2. Does this elevator appear to be safe?
High probability of the elevator being overloaded, so not safe. Correct answer is given by option D.
The width of a golden rectangle is 4 cm. Find the length of the rectangle to the nearest tenth of a centimeter. (Remember the golden ratio, 1.618.)
2.5 cm
6.5 cm
8 cm
13 cm
5.6 cm
Answer:
6.47
1.618 x 4 = 6.47
Step-by-step explanation:
Answer:
The length of golden rectangle is 6.5 cm.
Step-by-step explanation:
Definition of golden rectangle
The Golden Rectangle, also known as the perfect rectangle by some, is a rectangle with the Golden Ratio as its length to width ratio. Many people consider this to be one of the most visually appealing geometric shapes. Many works of art and architecture contain it.
Given the width of golden rectangle= 4 cm
and the golden ratio= 1.618
The golden ratio is the ratio of length and width [tex]l/b=1.618[/tex]
[tex]l=1.618*b\\=1.618*4\\=6.472 cm[/tex]
Now length of the rectangle is up to nearest tenth point=6.5 cm
Hence the length= 6.5 cm
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Suppose we have two thermometers. One thermometer is very precise but is delicate and heavy (X). We have another thermometer that is much cheaper and lighter, but of unknown precision (Y). We would like to know if we can (reliably) bring the lighter thermometer with us into the field. So, we set up an experiment where we expose both thermometers to 31 different temperatures and measure the temperature with each. We get the following observations:
x = 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120
y = 0.02, 3.99, 7.91, 12.03, 16.09, 20.00, 23.98, 28.09, 31.94, 36.03, 40.00, 44.05, 47.95, 52.00, 55.87, 59.90, 63.91, 67.95, 72.11, 76.02, 80.01, 84.10, 88.06, 91.74, 96.02, 99.95, 103.87, 108.01, 111.99, 116.04, 120.03
We want to test if these thermometers seem to be measuring the same temperatures. Let's use the threshold.
(a) Write down the appropriate hypothesis tests for β1.
H0: β1(≠ / = / > / <) 1 and Ha: β1( ≤ / = / > / ≠ / ≥ / <) 1.
(b) The test statistic is____.
(c) The p-value is____.
(d) Therefore, we can conclude that:_____.
1) The data provides evidence at the 0.1 significance level that these thermometers are not consistent.
2) The data provides no evidence at the 0.1 significance level that these thermometers are not consistent.
3) The probability that the null hypothesis is true is equal to the p-value.
4) The probability that we have made a mistake is equal to 0.1.
Answer:
a)H0: β1= 1 and Ha: β1 ≠1
b) The test statistic is____.t= b- β/ sb
c) The p-value is____.0.999144
(d) Therefore, we can conclude that:_____. there is not enough evidence to reject the null hypothesis.
2) The data provides no evidence at the 0.1 significance level that these thermometers are not consistent.
Step-by-step explanation:
The null and alternate hypotheses are
H0: β1= 1 and Ha: β1 ≠1
The significance level is alpha= 0.1 but ∝/2 =0.1/2= 0.05 for two tailed test.
The critical region at t ∝/2 (29)= t ≤ - 1.699 , t ≥ 1.699
The test statistic is
t= b- β/ sb
which has t distribution with υ= 31-2= 29 degrees of freedom.
Calculations
Ŷ = a +bX
b = SPxy /SS x= Σ(xi-x`)(yi-y`)/Σ(xi-x`)²
b = 39671.6/39680= 0.9998
a = y` - bx`
x`= 60
y`= 59.989
a = 59.989 -0.9998*60 = 0.001734
Syx²= Σ( yi -y`)²/ n-2= 39663.3857/ 29=1367.68965
Syx= 36.9822
Sb= Syx/ √∑ (x-x`)²
Sb= 36.9823/ √39680
Sb= 36.9823/ 199.984
Sb= 0.18493
x-x` y-y` (x-x`)² (x-x`)(y-y`)
-60 -59.969 3600 3598.1419
-56 -55.999 3136 3135.9458
-52 -52.079 2704 2708.1097
-48 -47.959 2304 2302.0335
-44 -43.899 1936 1931.5574
-40 -39.989 1600 1599.5613
-36 -36.009 1296 1296.3252
-32 -31.899 1024 1020.769
-28 -28.049 784 785.3729
-24 -23.959 576 575.0168
-20 -19.989 400 399.7806
-16 -15.939 256 255.0245
-12 -12.039 144 144.4684
-8 -7.989 64 63.9123
-4 -4.119 16 16.4761
0 -0.08903 0 0
4 3.921 16 15.6839
8 7.961 64 63.6877
12 12.121 144 145.4516
16 16.031 256 256.4955
20 20.021 400 400.4194
24 24.111 576 578.6632
28 28.071 784 785.9871
32 31.751 1024 1016.031
36 36.031 1296 1297.1148
40 39.961 1600 1598.4387
44 43.881 1936 1930.7626
48 48.021 2304 2305.0065
52 52.001 2704 2704.0503
56 56.051 3136 3138.8542
60 60.041 3600 3602.4581
∑0 0 39680 (SSx) 39671.6 (SPxy)
Putting the values
The test statistic is
t= b- β/ sb
t= 0.9998-1/ 0.18493 ( β=1 given)
t=-0.0010815
Since the calculated t=-0.0010815 does not lie in the critical region t ∝/2 (29)= t ≤ - 1.699 , t ≥ 1.699 we conclude that these thermometers seem to be measure temperatures.
The p-value is ≈ 0.999144
there is not enough evidence to reject the null hypothesis.
All the songs all the figures except a _____ have to bases
Answer:
Square pyramid
Step-by-step explanation:
The following data describes weekly gross revenue (), television advertising expenditures (), and newspaper advertising expenditures () for Showtime Movie Theaters.
Weekly Gross Revenue ($1000s) Televison Advertising ($1000s) Newspaper Advertising ($1000s)
98 5 1.5
90 2 2
95 4 1.5
92 2.5 2.5
95 3 3.3
94 3.5 2.3
94 2.5 4.2
94 3 2.5
Required:
Find an estimated regression equation relating weekdy gross revenue to television advertising expenditures and newspaper advertising expenditures (to 2 decimals).
Answer:
Hope this helps
Step-by-step explanation:
MRK ME BRAINLIEST PLZZZZZZZZZZZZZZ
Solve this exercise using the fact that the sum of the measures of the three angles of a triangle is 180.
In a triangle, the measures of the three angles are x, x+5, and x-35. What is the measure of each angle?
Answer:
X=70
Step-by-step explanation:
70 + 75 + 35 =180
x + x+5 + x-35
8y - (5y + 13 ) = -7
Answer:
y=2
Step-by-step explanation:
8y-5y-13=-7
3y-13=7
3y=-7+13
3y=6 /3
y=2
At a small savings and loan company, you have to deal with your customers being victims of identity theft. This happens unpredictably to one of your customers once every 9 weeks; and no incident seems to have any connection to any other incident. a) What is the probability that you will have to deal with no more than 4 incidents of identity theft in the next year (52 weeks)
Answer:
At a small savings and loan company, you have to deal with your customers being victims of identity theft. This happens unpredictably to one of your customers once every 9 weeks; and no incident seems to have any connection to any other incident.
Step-by-step explanation:
The probability that you will have to deal with no more than 4 incidents of identity theft in the next year is 30.08 %
What is a Binomial Distribution?
The binomial distribution is a type of probability distribution that predicts the likelihood of obtaining one of two outcomes given a set of inputs. It summarizes the number of tries where each trial has the equal chance of producing the same result.
The formula for Binomial Distribution is given by
P ( x ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ
where
n = number of trials
x = number of successes
p = probability of getting a success in one trial
q = probability of getting a failure in one trial
q = 1 - p
Given data ,
Let the probability that you will have to deal with no more than 4 incidents be P ( x ≤ 4 )
Now , the success is one of your customers once every 9 weeks
So , p = 1/9
q = 1 - p = 8/9
x = 4
Number of trials n = 52 weeks
And , the probability that you will have to deal with no more than 4 incidents be P ( x ≤ 4 ) is
P ( x ≤ 4 ) = [ n! / ( n - x )! x! ] pˣqⁿ⁻ˣ
Substituting the values in the equation , we get
P ( x ≤ 4 ) = [ 52! / ( 48 )! 4! ] ( 1/9 )⁴( 8/9 )⁴⁸
On simplifying the equation , we get
P ( x ≤ 4 ) = 0.3008
P ( x ≤ 4 ) = 30.08 %
Therefore , the value of P ( x ≤ 4 ) is 30.08 %
Hence , the probability of no more than 4 incidents is 30.08 %
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The original price of a skateboard, not including tax, was $96. Charlie bought the skateboard on sale, and he saved 30% off of the original price.
What was the sale price of the skateboard?
Answer:
The sale price was $67.20
Step-by-step explanation:
The sale price is 30% less than the original price. Symbolically,
Sale price: (100% less 30%) of $96, or
(1.00 - 0.30)($96), or 0.70($96) = $67.20
The sale price was $67.20
A billing company that collects bills for doctors' offices in the area is concerned that the percentage of bills being paid by medical insurance has risen. Historically, that percentage has been 31%. An examination of 8,606 recent, randomly selected bills reveals that 32% of these bills are being paid by medical insurance. Is there evidence of a change in the percent of bills being paid by medical insurance
Answer:
Following are the responses to the given question:
Step-by-step explanation:
[tex]H_o : p =0.31\\\\H_a: p \neq 0.31\\\\n = 8606 \\\\ p^ = 0.32[/tex]
[tex]TS = \frac{(p^ - p)}{\sqrt{(\frac{pq}{n})}}[/tex]
[tex]= \frac{(0.32-0.31)}{\sqrt{(\frac{0.31\times 0.69}{8368})}}\\\\=\frac{0.01}{5.4}\\\\=0.00185\\\\[/tex]
Use words to explain how to multiply (3^3) (3^4).
Pls help
Answer:
9^7
Step-by-step explanation:
Multiple the two 3's and get 9 then when you multiply exponents you add them and get 7
What is six times six
Answer:
36
Step-by-step explanation:
6+6+6+6+6+6=36
Andre has a container that is 10 inches wide 8 inches high and 14 inches deep he wants to fill the container with packages that are 5 inches wide 4 inches high 2 inches deep what is the greatest number of packages that he could put in the container
HELP PLEASE write an equation of the ellipse with foci at (0 ±10) and vertices at (0 ±11)
The equation of the ellipse with foci at (0 ±10) and vertices at (0 ±11) is [tex]\frac{x^2}{21} + \frac{y^2}{100} = 1[/tex]
How to determine the ellipse equation?We have:
Vertices = (0, ± 11),
Foci = (0, ± 10)
The vertices and the foci are represented as:
Foci = (0, ± a)
Vertices = (0, ± c)
So, we have:
a = 10
c = 11
The equation of b is calculated using:
b² = c²- a²
So, we have:
b² = 11²- 10²
Evaluate
b² = 21
The equation of the ellipse is then represented as:
[tex]\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1[/tex]
This gives
[tex]\frac{x^2}{21} + \frac{y^2}{10^2} = 1[/tex]
[tex]\frac{x^2}{21} + \frac{y^2}{100} = 1[/tex]
Hence, the equation of the ellipse is [tex]\frac{x^2}{21} + \frac{y^2}{100} = 1[/tex]
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Answer:
x^2/221+Y^2/121=1
Step-by-step explanation:
Composite scores on the ACT are normally distributed with a mean of 21 and a standard deviation of 5. find the Z score for a student that gets a 31
Answer:
[tex]Z = 2[/tex]
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 21 and a standard deviation of 5.
This means that [tex]\mu = 21, \sigma = 5[/tex]
Find the Z score for a student that gets a 31
This is Z when X = 31. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{31 - 21}{5}[/tex]
[tex]Z = 2[/tex]
A helicopter pad has a circumference of 47.5 yards. Find the approximate diameter of the helicopter pad. Use 3.14 for π.
The approximate diameter of the helicopter pad is 15.13 yards.
We can use the formula for a circle's circumference, C = πd , where C is the circumference, d is the diameter, and π is a constant equivalent to roughly 3.14, to determine the estimated diameter of the helicopter pad.We can use the method to solve for the diameter if we know the helicopter pad's circumference to be 47.5 yards. After rearranging the equation, we get d = C/π.Thus, using the provided values as a substitute, we obtain d = 47.5/3.14 = 15.13 yards. (rounded to two decimal places).As a result, the helicopter pad's estimated diameter is 15.13 yards.
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A smartphone costs $250. Sales tax is 7%. What is the total cost, including tax?
The cost of the smartphone, with tax, is $
Answer:17.5
Step-by-step explanation:
Our output value is 250
We represent the unknown value wit “x”
250= 100%
x= 7%
By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both
equations have the same unit (%); we have
250/x = 100%/7%
Again, the reciprocal of both sides gives
x/250= 7/100
X= 17.5
17.5=7% of 250
Find the m2.
O a. m Q = 30 degrees
O b.mxQ = 60 degrees
O c. m Q = 70 degrees
O d. m2Q = 75 degrees
9514 1404 393
Answer:
d. m∠Q = 75 degrees
Step-by-step explanation:
The sum of the angles in a triangle is 180°. This triangle is marked to show it is an isosceles triangle, so the two base angles have the same measure.
∠P +∠Q +∠R = 180°
x° +(2x +15)° +(2x +15)° = 180°
5x = 150 . . . . . . . . . . . . . . . . . . . divide by °, subtract 30
x = 30 . . . . . . . . . . . . . . . . divide by 5
m∠Q = (2x +15)° = (2(30) +15)°
m∠Q = 75°
Classify each triangle by side length and angle measure.
Answer:
Below.
Step-by-step explanation:
1. Isosceles.
2. Scalene
3. Equilateral.
4. Right triangle.
Please help me :( I feel worthless because of math
Answer:
I think 262 is the right answer.
Step-by-step explanation:
Don't feel worthless because of math! Math is a diffcult to understand subject, and a real pain in the butt.
The angles in this diagram are complementary. What is the value of x?
(4x)
(2x + 6)
Answer:
2(4)+6(4)
Step-by-step explanation:
Distribute
(4)(2+6)
(4x)(2x+6)2(4)+6(4)
2x(4x)+6(4x)
Solution
2(4)+6(4)
Please give brainliest :)
If a normal 6 sided die, with each side numbered 1 through 6, is rolled. What is the probability that the number on top is greater than 3?
Select one:
1/6
1/2
1/3
2/3
Answer: the second option (1/2)
Step-by-step explanation:
numbers greater than 3: 4, 5, and 6
3 numbers
so 3/6 or 1/2
1/2 or 50% so the second option
[2x(3+5)+6]x4 what is the value of this expression
Answer:
16x5+6x4
Step-by-step explanation:
(2x(3+5)+6)(x4)
=(2x(3+5)+6)(x4)
=(2x(3+5))(x4)+(6)(x4)
=16x5+6x4
Answer:
88
Step-by-step explanation:
to solve these kind of questions use BODMAS
WILL
GIVE
BRAINLIST
.
..
.
.
..
Answer:
1/6
Step-by-step explanation:
Given the following data;
A single fair die = 6
To find an outcome of A5;
Since the die was tossed just once, the outcome would be a fraction of the total number of outcomes.
P(A5) = number of times tossed/total number of outcomes
P(A5) = 1/6
Perform the indicated operation. -6 + 6
Answer:
0
Step-by-step explanation:
It is zero, since -6+6 is bassicly 6-6 which is 0
As part of the quality-control program for a catalyst manufacturing line, the raw materials (alumina and a binder) are tested for purity. The process requires that the purity of the alumina be greater than 84%. A random sample from a recent shipment of alumina yielded the following results (in percent):
93.2, 87.0, 92.1, 90.1, 87.1, and 93.4.
A hypothesis test will be done to determine whether or not to accept the shipment.
a. State the appropriate null and alternate hypotheses.
b. Compute the P-value.
c. Should the shipment be accepted? Explain.
Determine whether the sampling is dependent or independent. Indicate whether the response variable is qualitative or quantitative.
A psychologist wants to measure the effect of music on memory. He randomly selects 80 students and measures their scores on a memory test conducted in silence. The next day he measures their scores on a similar test conducted while classical music is playing. The mean score without music is compared to the mean score with music.
A. quantitative, independent.
B. quantitative, dependent.
C. qualitative, dependent.
D. qualitative, independent.
Answer:
its B i did chapter 11 test yesterday
Step-by-step explanation:
A circle has a diameter of 8.2 m. What is the area of a sector with a 125 degree
arc? Round your answer to the nearest tenth. *
Answer:24.2 m
Step-by-step explanation: yea u gotta use the metric system
5 fractions with denominator of 1 between 0 and 1/14
Answer:
Are there options to choose from?
Step-by-step explanation:
1
1
1
4
2
4
2
2
3
9
343
4 16
4
1
B
D
y
ху
1 12
1 3
2
1
25
3 3/2
37
4
2
9
Which table shows y as DIRECTLY PROPORTIONAL tox?
0
A)
A
B)
B
D
D
D
Answer:
what are you trying to do or say
Use the simple interest formula i= prt. What is the value of i, if p=$6000, r=5%, and t= 3 years
Answer: $6,945.75
6000(1+.05)^3