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3 years ago

The box plots below show attendance at a local movie theater and high school basketball games:

Mathematics

2 answers:

dlinn [17]3 years ago

8 0

Answer:

<h2>D. The standard deviation is the best measurement of spread for games and movies.</h2>

Step-by-step explanation:

Measures of spread are stats that describes how separated are the group of data between each other.

The measures are range, quartiles, variance and standard deviation. Among these measures, the standard deviation is the one that best expresses the variation, dispersion or spread of a set of values, because is based on the difference between each data and the mean, it takes in count each separation.

That's why the correct answer is D.

Firdavs [7]3 years ago

7 0

Assume that the data for both movies and basketball games are normally distributed.
Therefore, the median and the mean are assumed equal.
The standard deviation, σ, is related to the interquartile range by
IQR = 1.35

From the data, we can say the following:

Movies:
Range = 150 - 60 = 90 (approx)
Q1 = 62 (approx), first quartile
Q3 = 120 (approx), third quartlie
Q2 (median) = 90 (approx)
IQR = Q3 - Q1 = 58
σ = IQR/1.35 = 58/1.35 = 43

Basketball:
Range = 150 - 90 = 60 approx
Q1 = 95 (approx)
Q3 = 145 (approx)
Q2 = 125 (approx)
IQR = 145 - 95 = 50
σ = 50/1.35 = 37

Test the given answers.
A. The IQRs are approximately equal, so they are not good measures of spread. This is not a good answer.
B. The std. deviation is a better measure of spread for basketball. This is not a good answer.
C. IQR is not a better measure of spread for basketball games. This is not a good answer.
D. The standard deviation is a good measure of spread for both movies and basketball. This is the best answer.

Answer: D

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Data collected at Toronto Pearson International Airport suggests that an exponential distribution with mean value 2725hours is a

Ivan

Answer:

a) What is the probability that the duration of a particular rainfall event at this location is at least 2 hours?

We want this probability"

$P(X >2) = 1-P(X\leq 2) = 1-(1- e^{-0.367 *2})=e^{-0.367 *2}= 0.48$

At most 3 hours?

$P(X \leq 3) = F(3) = 1-e^{-0.367*3}= 1-0.333 =0.667$

b) What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations?

$P(X > 2.725 + 2*5.540) = P(X>13.62) = 1-P(X$

What is the probability that it is less than the mean value by more than one standard deviation?

$P(X$

Step-by-step explanation:

Previous concepts

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

$P(X=x)=\lambda e^{-\lambda x}$

The cumulative distribution for this function is given by:

$F(X) = 1- e^{-\lambda x}, x\ geq 0$

We know the value for the mean on this case we have that :

$mean = \frac{1}{\lambda}$

$\lambda = \frac{1}{Mean}= \frac{1}{2.725}=0.367$

Solution to the problem

Part a

What is the probability that the duration of a particular rainfall event at this location is at least 2 hours?

We want this probability"

$P(X >2) = 1-P(X\leq 2) = 1-(1- e^{-0.367 *2})=e^{-0.367 *2}= 0.48$

At most 3 hours?

$P(X \leq 3) = F(3) = 1-e^{-0.367*3}= 1-0.333 =0.667$

Part b

What is the probability that rainfall duration exceeds the mean value by more than 2 standard deviations?

The variance for the esponential distribution is given by: $Var(X) =\frac{1}{\lambda^2}$

And the deviation would be:

$Sd(X) = \frac{1}{\lambda}= \frac{1}{0.367}= 2.725$

And the mean is given by $Mean = 2.725$

Two deviations correspond to 5.540, so we want this probability:

$P(X > 2.725 + 2*5.540) = P(X>13.62) = 1-P(X$

What is the probability that it is less than the mean value by more than one standard deviation?

For this case we want this probablity:

$P(X$

8 0

4 years ago

Write the equation 12 − y = 2x − 5 in slope-intercept form. What are the slope and y-intercept? A. y=2x−17,m=2, y-intercept (0,−

MrRissso [65]

Answer:

Step-by-step explanation:

12-y=2x-5

+5 +5 ( add 5 to both sides)

17-y=2x

-17 -17 (Subtract 17 to get y by itself)

-y=2x-17

divide by -1 because y cant be negative

y=-2x+17

m=-2 and y-intercept= 17

I hope thats right :)

8 0

3 years ago

Use the difference of squares pattern to factor the polynomial.x2 − 16y2 how would I do this

love history [14]

The general rule for difference of two squares is that when factorised it can be written in the form (a+b)(a-b) where a is the square root of the first part of the function and b is the square root of the second part of the function.
From this we can find the square root of x² to find a and the square root of 16y² to find b.
In this case √x²=x and √16y²=4y
Therefore fully factorised it can be written as (x+4y)(x-4y)

6 0

3 years ago

A recommendation for wheelchair ramps is that the rise-to-run ratio be no greater than 1:12. This ensures that the ramps are nav

patriot [66]

Answer:

a. 12 feet b. 12 feet 0.5 inches c. 8.33 %

Step-by-step explanation:

a. How far out horizontally on the ground will it protrude from the building?

Since the rise to run ratio is 1:12 and the building is 12 inches off the ground, let x be the horizontal distance the ramp protrudes.

So, by ratios rise/run = 1/12 = 12/x

1/12 = 12/x

x = 12 × 12

x = 144 inches

Since 12 inches = 1 foot, 144 inches = 144 × 1 inch = 144 × 1 foot/12 inches = 12 feet

b. How long should the ramp be?

The length of the ramp, L is gotten from Pythagoras' theorem since the ramp is a right-angled triangle with sides 12 inches and 144 inches respectively.

So, L = √(12² + 144²)

= √[12² + (12² × 12²)]

= 12√(1 + 144)

= 12√145

= 12 × 12.042

= 144.5 inches

Since 12 inches = 1 foot, 144.5 inches = 144 × 1 inch + 0.5 inches = 144 × 1 foot/12 inches + 0.5 inches = 12 feet 0.5 inches

c. What percent grade is the ramp?

The percentage grade of the ramp = rise/run × 100 %

= 12 inches/144 inches × 100 %

= 1/12 × 100 %

= 0.0833 × 100 %

= 8.33 %

6 0

3 years ago

Y=x^2+3x-4 and y=4x-4

sweet [91]

The answer is (0,-4),(1,0)

8 0

3 years ago