let X represent the amount of time till the next student will arriv ein the library partking lot at the university. If we know that the dstubtion of arrivlal time can be modeled using an exponential distruibution with a mean of 4 minutes, find the probabiity that it will take between 2 and 132 minutes for the net sutedn to arrive at the library partking lot 0.606531

Answers

Answer 1

Answer:

0.606531 = 60.6531% probability that it will take between 2 and 132 minutes for the student to arrive at the library parking lot.

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

Mean of 4 minutes

This means that [tex]m = 4, \mu = \frac{1}{4} = 0.25[/tex]

Find the probability that it will take between 2 and 132 minutes for the student to arrive at the library parking lot:

This is:

[tex]P(2 \leq X \leq 132) = P(X \leq 132) - P(X \leq 2)[/tex]

In which

[tex]P(X \leq 132) = 1 - e^{-0.25*132} = 1[/tex]

[tex]P(X \leq 2) = 1 - e^{-0.25*2} = 0.393469[/tex]

[tex]P(2 \leq X \leq 132) = P(X \leq 132) - P(X \leq 2) = 1 - 0.393469 = 0.606531[/tex]

0.606531 = 60.6531% probability that it will take between 2 and 132 minutes for the student to arrive at the library parking lot.


Related Questions

A cone has the same radius and height as a cylinder which has greater volume the cone or the cylinder

Answers

Answer:

The cylinder has the great volume

Step-by-step explanation:

The volume of a cone = (h/3)πr²

The volume of a cylinder = hπr²

The only difference is that h is divided by 3 for the volume of a cone, making the total volume of a cone smaller than the volume of a cylinder with the same radius and height.

The calibration of a scale is to be checked by weighing a 13 kg test specimen 25 times. Suppose that the results of different weighings are independent of one another and that the weight on each trial is normally distributed with Sigma = 0.200 kg. Let µ denote the true average weight reading on the scale.

Required:
a. What hypotheses should be tested?
b. With the sample mean itself as the test statistic, what is the P-value?

Answers

Solution :

a).

Given : Number of times, n = 25

            Sigma, σ = 0.200 kg

            Weight, μ = 13 kg

Therefore the hypothesis should be tested are :

[tex]$H_0 : \mu = 13 $[/tex]

[tex]$H_a : \mu \neq 13$[/tex]

b). When the value of [tex]$\overline x = 12.84$[/tex]

 Test statics :

   [tex]$Z=\frac{(\overline x - \mu)}{\frac{\sigma}{\sqrt n}} $[/tex]

  [tex]$Z=\frac{(14.82-13)}{\frac{0.2}{\sqrt {25}}} $[/tex]

          [tex]$=\frac{1.82}{0.04}$[/tex]

          = 45.5  

P-value = 2 x P(Z > 45.5)

            = 2 x 1 -P (Z < 45.5) = 0

Reject the null hypothesis if P value  < α = 0.01 level of significance.

So reject the null hypothesis.

Therefore, we conclude that the true mean measured weight differs from 13 kg.

Mary is having her living room and bedroom painted. Interior Designs USA charges $60.00 to evaluate the space plus $35.00 per hour of labor. Splash of Color charges $55.00 per hour with no initial fee. Which of the following are true? Select all that apply.

A) If it takes 7 hours to paint the two rooms, Interior Designs USA will charge the least.
B) Splash of Color will always charge the least.
C) If it takes more than 5 hours to paint the rooms, Splash of Color will be more cost effective.
D) If it takes 10 hours to paint the rooms, Splash of Color will charge $200 more than Interior Designs USA.
E) If it takes 3 hours to paint the rooms, both companies will charge the same amount.

Answers

Answer:

A and E

Step-by-step explanation:

A) 7 hrs in IDU will cost you $305.00 while SC cost $385

B) 4hrs in and SC will charge you more than IDU by $20

C) SC charges you more than IDU by $50 so IDU is more cost effective

D)SC will charge you $140 more than IDU but not $200

E) 55 x 3 = 165 while 35 × 3 105 plus 60 is 165 therefore it is the same

"Jonas prepared himself to walk to the stage when the applause ended and the Chief Elder picked up the next folder and looked down to the group to call forward the next new Twelve. He was calm now that his turn had come. He took a deep breath and smoothed his hair with his hand." - The Giver *

1st person
2nd person
3rd person objective
3rd person limited
3rd person omniscient

Answers

Answer:

3rd limited

Step-by-step explanation:

Suppose that 55% of people own dogs. If you pick two people at random, what is the probability that they both own a dog?

Answers

Answer:

The probability to one person to be a dog owner is p=0.56 (because 56% of people own dogs) and the probability that one person is not dog owner is q=1-p=1-0.56=0.44.

Step-by-step explanation:

Choosing two people at random, there are such possibilities:

1. both are dog owners;

2. first owns a dog, second not;

3. first hasn't dog, second owns a dog;

4. both haven't dogs.

Answer: if you pick two people at random the probability that they both own a dog is 0.3136.

Hope this helps! :))

The Probability that they both own a dog is 0.3025.

Here,

55% of people own dogs.

If pick two people at random,

Then we have to find the probability that they both own a dog.

What is Probability?

Probability is defined as the likelihood of something occurring or the chance of something happening.

Now,

55% of people own dogs.

Hence, the probability that they both own a dog = 55% * 55%

                                                                          = 0.55 * 0.55

                                                                          = 0.3025

So, The probability that they both own a dog is 0.3025.

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What is the volume of a cylinder with base radius 2 and height 5?
Either enter an exact answer in terms of 3.14 for pi

Answers

Answer:

V ≈ 62.83

Step-by-step explanation:

Cylinder Formulas in terms of r and h

Calculate the volume of a cylinder:

V = πr2h

Calculate the lateral surface area of a cylinder (just the curved outside):

L = 2πrh

Calculate the top and bottom surface area of a cylinder (2 circles):

T = B = πr2

Total surface area of a closed cylinder is:

A = L + T + B = 2πrh + 2(πr2) = 2πr(h+r)

Solution

V=πr 2h = π · 22 · 5 ≈ 62.83185

Therefore, the volume of the cylinder in the nearest tenths is V ≈ 62.83

What type of triangle is this if lengths of its sides are 37m, 24m, and 5m *​

Answers

Answer:

weird triangle

Step-by-step explanation:

Answer:

Scalene triangle

Step-by-step explanation:

Scalene triangle: If the length of all the sides of triangle have  different measurements then it is scalene triangle

An introductory psychology class has 9 freshman males, 15 freshman females, 8 sophomore males, and 12 sophomore females. A random sample of n = 2 students is selected from the class. If the first student in the sample is a male, what is the probability that the second student will also be a male?

Answers

Answer

16/43

Step-by-step explanation:

17 Male + 27 female = 44 students

now n= 2 so first student was male so one male student was taken out of the equation so 16 male left. now left male students by remaining students  so now total left students = 43

so, prob = remaining males/remaining students=16/43

Where do I put the parentheses in 15-3x4+9=12

Answers

Answer:

That depends on which operations you want to do first. The order of operations affect to outcome of the equation.

In this case:

15 - (3 x 4) + 9 = 12

Answer:

It varies but this is one example

15 - (3 x 4) + 9 = 12

plz mark as brainliest

NO LINKS!! URGENT HELP PLEASE!!!

Determine if the scenario involves mutually exclusive events.

32. A cooler contains 12 bottles of sports drinks: 4 lemon-lime flavored, 3 orange-flavored, and 5 fruit-punch flavored. You grab a bottle. It is a lemon-lime or an orange.

33. Find the 5 number summary (Min, Q1, Median, Q3, Max) for the following data and draw a box and whisker graph.

18, 24, 28, 28, 36, 44, 50, 67

Answers

Answer:

32)  7/12 ≈ 58.3%

33)  Min = 18
       Q1 = 26
       Median = 32
       Q3 = 47
       Max = 67

Step-by-step explanation:

Question 32

To determine the probability of grabbing a lemon-lime or an orange-flavored bottle from the cooler, we need to calculate the number of favorable outcomes and the total number of possible outcomes.

In the given scenario, there are 4 lemon-lime flavored bottles and 3 orange-flavored bottles in the cooler, plus 5 fruit-punch flavored bottles. Therefore:

Number of favorable outcomes = 4 + 3 = 7Total number of bottles = 4 + 3 + 5 = 12

The probability of grabbing a lemon-lime or an orange-flavored bottle is:

[tex]\begin{aligned}\sf Probability &= \sf \dfrac{Favorable\;outcomes}{Total\; outcomes}\\\\&=\dfrac{7}{12}\\\\& \approx 58.3\%\end{aligned}[/tex]

[tex]\hrulefill[/tex]

Question 33

The five-number summary is a statistical summary of a dataset that includes the minimum and maximum values, the median (middle value), and the first and third quartiles. It provides a concise overview of the distribution and central tendency of the data.

First, sort the given data in ascending order (this has already been done for us):

18, 24, 28, 28, 36, 44, 50, 67

Minimum value

The minimum value is the smallest value in the data set.

[tex]\boxed{\sf Minimum \; value = 18}[/tex]

Median

The median is the middle value of the sorted data.

In this case, we have 8 data points, so the median is the average of the two middle values:

[tex]\boxed{\sf Median\;(Q_2)=\dfrac{28+36}{2}=32}[/tex]

First Quartile (Q₁)

The first quartile is the median of the lower half of the data.

In this case, we have 4 data points in the lower half (18, 24, 28, 28), so the median is the average of the two middle values:

[tex]\boxed{\sf First \;Quartile\;(Q_1)=\dfrac{24+28}{2}=26}[/tex]

Third Quartile (Q₁)

The third quartile is the median of the upper half of the data.

In this case, we have 4 data points in the upper half (36, 44, 50, 67), so the median is the average of the two middle values:

[tex]\boxed{\sf Third\;Quartile\;(Q_3)=\dfrac{44+50}{2}=47}[/tex]

Maximum value

The maximum value is the largest value in the data set.

[tex]\boxed{\sf Maximum\; value = 67}[/tex]

Therefore, the five-number summary for the given data set is:

Min = 18Q₁ = 26Median = 32Q₃ = 47Max = 67

To construct the box and whisker graph (attached):

Draw a box from the lower quartile (26) to the upper quartile (47).Add the median (32) as a vertical line through the box.The whiskers are horizontal lines from each quartile to the minimum (18) and maximum values (67).

The events are mutually exclusive because a bottle cannot be both lemon-lime and orange-flavored simultaneously , the scenario involves mutually exclusive events.

The five-number summary is as follows:

Minimum: 18

Q1: 26

Median: 36

Q3: 47

Maximum: 67

The scenario states that there are 12 bottles of sports drinks in a cooler: 4 lemon-lime flavored, 3 orange-flavored, and 5 fruit-punch flavored. You grab a bottle, and it is either lemon-lime or orange flavored. To determine if this scenario involves mutually exclusive events, we need to assess whether the two events (grabbing a lemon-lime flavored bottle and grabbing an orange-flavored bottle) can occur at the same time or not.

In this case, the events are mutually exclusive because a bottle cannot be both lemon-lime and orange-flavored simultaneously. Therefore, the scenario involves mutually exclusive events.

To find the five-number summary (minimum, first quartile, median, third quartile, and maximum) for the given data and draw a box and whisker plot, we need to arrange the data in ascending order first:

18, 24, 28, 28, 36, 44, 50, 67

Arranging the data in ascending order: 18, 24, 28, 28, 36, 44, 50, 67

The minimum value is 18.

The first quartile (Q1) is the median of the lower half of the data: (24 + 28) / 2 = 26.

The median is the middle value of the data set: 36.

The third quartile (Q3) is the median of the upper half of the data: (44 + 50) / 2 = 47.

The maximum value is 67.

The five-number summary is as follows:

Minimum: 18

Q1: 26

Median: 36

Q3: 47

Maximum: 67

To draw a box and whisker plot, you can use the five-number summary to create a visual representation of the data distribution. However, since I can't draw graphs here, you can create a box and whisker plot yourself. Draw a number line and place a box that spans from Q1 to Q3, with a line inside representing the median. Add "whiskers" extending from the box to the minimum and maximum values.

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convert 2x + y = -1 to slope intercept form

Answers

Answer:

y=-2x-1

Step-by-step explanation:

Your goal from Standard form to slope intercept form is to have the x on the right side of the equal sign. All you have to do is subtract 2x from both sides and you end up with y= -2x-1

Valentina buys a chandelier priced at $713. If the sales tax is 4%, how
much tax will
Valentina pay?​

Answers

Answer:

$741.52 TRUSTTT

Step-by-step explanation:

Answer:

x + (tax percent out of 100)*x, which is 748.65.

Witch is larger? 1/3 or 3/9

Answers

1/3 give me branliesttt

Answer:

they are equal

Step-by-step explanation:

1/3 to a decimal is 0.333

3/9 is 0.333

so they are the same the person above me is wrong

Find the area of the regular octagon with radius of 14
feet.


Answers

Answer:

uhm- ok ok ok level hard o my gosh

What is y if x=6 eqaution=y=4x+5​

Answers

y=29 ! hope this helps

A rectangular billboard for a high school is 10 feet high and 20 feet long. In a scale model of the school, the billboard is 3.5 inches long.
How many inches tall is the scale model? ​

Answers

Answer:

I think 1.75

Step-by-step explanation:

the long side is two times the amount of the tall side so take the smaller long side and divide by two.

I am not good at math, will give brainliest

Answers

Answer:

the answer is a

Step-by-step explanation:

Write a jingle to advertise
favorite dessert to the tune of
"Twinkle, Twinkle Little Star."
What is so special about this
dessert? How can you describe it
in a memorable, catchy way?

Y’all someone help no link ,will be reported

Answers

My Jingle:

Ice cream cake - oh, ice cream cake...

How I love the way you taste...

You melt in my mouth with every bite...

Dreams of you keep me up at night...

Ice cream cake - oh, ice cream cake...

How I love the way you taste.

I hope you like it!

What is the area of this figure? I give brainliest :)

Answers

Answer:

[tex] 217 \: {mi}^{2} [/tex]

Step-by-step explanation:

Area of the figure

[tex]= 13*7 + 21 * 6 \\ = 91 +12 6 \\ = 217 \: {mi}^{2} [/tex]

Can someone help me with this?

Answers

9514 1404 393

Answer:

  π/4, 7π/4

Step-by-step explanation:

Adding √2 and dividing by 2 makes the equation ...

  cos(θ) = (√2)/2

The first-quadrant solution is ...

  θ = arccos((√2)/2) = π/4

The angle in the 4th quadrant with the same reference angle will have the same cosine value.

  θ = 2π -π/4 = 7π/4

The two solutions are θ = π/4, 7π/4.


Please help ASAP please help

Answers

Answer:

64

Step-by-step explanation:

8x4 is 32 multiplied by 2 is 64

V=LxWxH

(length x Width x Height)

Hey I need help .. again we’re doing log lines

Answers

Answer:

Step-by-step explanation:

40 POINTS !! 40 POINTS !!

PLEASE HELP , DONT SKIP !

NO LINKS OR FILES.

Answers

Answer:

Step-by-step explanation:

Answer:

the size of the matrix 2x3

Step-by-step explanation:

just remember that rows are horizontal and columns are vertical hope this helps you out

(-6, -7) and (3,-4)
Pleaseee helppppppp​

Answers

Answer:

y = x/3 - 5

Step-by-step explanation:

Answer:

y = (1/3)x  - 5 .

Step-by-step explanation:

(-6 , -7) ; (3 ,-4)

Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\[/tex]

          [tex]=\frac{-4-[-7]}{3-[-6]}\\\\= \frac{-4 + 7}{3+6}\\\\= \frac{3}{9}\\\\=\frac{1}{3}[/tex]

m = 1/3   ; (3,-4)

y - y1 = m(x - x1)

[tex]y - [-4]=\frac{1}{3}(x-3)\\\\y + 4 = \frac{1}{3}x-3*\frac{1}{3}\\\\y + 4 = \frac{1}{3}x-1\\\\y =\frac{1}{3}x-1-4\\\\y = \frac{1}{3}x - 5[/tex]

Help Plis ...............

Answers

Answer:

it is positive 3/4

Step-by-step explanation:

it is the opposite of -3/4

Answer:

it would be a positive 3/4

Please help me if you can!

Answers

Mrs. Duran had $665 at the end of the day

Zachary's rectangle measures 4 1 /4 units by 4 1 /4 units. What is its area?

Answers

Answer:

169/12 square units.

Step-by-step explanation:

the equation p=52+0.04w models relation between the amount of water bill payment p in dollars and the number of units of water w in slope of equation

Answers

The slope in the equation p = 52 + 0.04w represents the rate of change in the water bill payment for each additional unit of water consumed.

Specifically, the slope of 0.04 indicates that for every increase of one unit in the number of water units (w), the water bill payment (p) will increase by 0.04 dollars.

This means that the slope represents the incremental cost of each additional unit of water.

In practical terms, the slope of 0.04 implies that for every additional unit of water consumed, the water bill will increase by $0.04.

This indicates a constant rate of increase in the water bill for each additional unit of water used.

It's important to note that the slope remains constant throughout the equation, suggesting a linear relationship between the amount of water consumed and the corresponding bill payment.

Therefore, The slope, in this case, is the coefficient of the variable w, which is 0.04.

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The probable question may be:

What is the meaning of the slope in the equation p = 52 + 0.04w, which models the relationship between the water bill payment p in dollars and the number of units of water w ?

Huh?! Its me DaBaby less gooo i need your help with this question. Yeah Yeah!

Answers

Answer:

[tex]4\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\sqrt{48} \\\\4\sqrt{3}[/tex]

Answer:

the second option is correct

Step-by-step explanation:

8. How tall is a stack of 26 coins each 0.03 m thick? ​

Answers

Answer:

0.78

Step-by-step explanation:

0.03*26=0.78 simple math lol

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