1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
expeople1 [14]
3 years ago
10

Finn changes his mind and, from now on, decides to take the normal route to work everyday. On any given day, the time (in minute

s) it takes Finn to get to work is normally distributed with mean u = 35 and variance = 81 .
Find the 33rd percentile of the time it takes Finn to get to work on any given day. Do not include any units in your answer.

Recall from Question 6 that on any given day, the time (in minutes) it takes Finn to get to work is normally distributed with mean = 35 and variance =81. Assume the time it takes him to get to work is independent from day to day.

Over the next 2 days, find the probability that Finn took more than 40.5 minutes to get to work on the first day or more than 38.5 minutes to get to work on the second day.
Mathematics
1 answer:
Margaret [11]3 years ago
7 0

Answer:

The 33rd percentile of the time it takes Finn to get to work on any given day is 31.04 minutes.

There is a 61.92% probability that Finn took more than 40.5 minutes to get to work on the first day or more than 38.5 minutes to get to work on the second day.

Step-by-step explanation:

This can be solved by the the z-score formula:

On a normaly distributed set with mean \mu and standard deviation \sigma, the z-score of a value X is given by:

Z = \frac{X - \mu}{\sigma}

Each z-score value has an equivalent p-value, that represents the percentile that the value X is:

The problem states that:

Mean = 35, so \mu = 35

Variance = 81. The standard deviation is the square root of the variance, so \sigma = \sqrt{81} = 9.

Find the 33rd percentile of the time it takes Finn to get to work on any given day. Do not include any units in your answer.

Looking at the z-score table, z = -0.44 has a pvalue of 0.333. So what is the value of X when z = -0.44.

Z = \frac{X - \mu}{\sigma}

-0.44 = \frac{X - 35}{9}

X - 35 = -3.96

X = 31.04

The 33rd percentile of the time it takes Finn to get to work on any given day is 31.04 minutes.

Over the next 2 days, find the probability that Finn took more than 40.5 minutes to get to work on the first day or more than 38.5 minutes to get to work on the second day.

P = P_{1} + P_{2}

P_{1} is the probability that Finn took more than 40.5 minutes to get to work on the first day. The first step to solve this problem is finding the z-value of X = 40.5.

Z = \frac{X - \mu}{\sigma}

Z = \frac{40.5 - 35}{9}

Z = 0.61

Z = 0.61 has a pvalue of 0.7291. This means that the probability that it took LESS than 40.5 minutes for Finn to get to work is 72.91%. The probability that it took more than 40.5 minutes if P_{1} = 100% - 72.91% = 27.09% = 0.2709

P_{2} is the probability that Finn took more than 38.5 minutes to get to work on the second day. Sine the probabilities are independent, we can solve it the same way we did for the first day, we find the z-score of

X = 38.5

Z = \frac{X - \mu}{\sigma}

Z = \frac{38.5 - 35}{9}

Z = 0.39

Z = 0.39 has a pvalue of 0.6517. This means that the probability that it took LESS than 38.5 minutes for Finn to get to work is 65.17%. The probability that it took more than 38 minutes if P_{1} = 100% - 65.17% = 34.83% = 0.3483

So:

P = P_{1} + P_{2} = 0.2709 + 0.3483 = 0.6192

There is a 61.92% probability that Finn took more than 40.5 minutes to get to work on the first day or more than 38.5 minutes to get to work on the second day.

You might be interested in
Find the equation of the line that passes through the pair of points(-1,-2),(-1,3)
Sliva [168]

Answer:

x = -1

Step-by-step explanation:

If both the x values are the same it will be a vertical line and the equation will be x = whatever the x value is in the ordered pair.

5 0
3 years ago
Look at the question
tamaranim1 [39]
Your answer is:

B. subtract 10 to both sides

Hope it helps
Have a great day :)
Let me know if it’s correct
5 0
3 years ago
melanie made a circular necklace she puts beads evenly spaced around the necklace if the 4th bead is directly across from the 11
dangina [55]

Answer:

Step-by-step explanation:

If the 4th lies opposite the 11th, then you know the 3rd lies opposite the 10th, the 2nd opposite the 9th, and the 1st opposite the 8th; meanwhile, in the reverse direction you'd find that the 5th lies opposite the 12th, the 6th opposite the 13th, and the 7th opposite the 14th. Move up one more bead and you're back at the 1st, which you already know lies opposite the 8th. Therefore there are 14 total bead

4 0
3 years ago
Which ratios are equal to 64 when the scale factor is 8? Select all that apply.
Luden [163]

Answer:

The scaled surface area of a square pyramid to the original surface area.

The scaled area of a triangle to the original area.

Step-by-step explanation:

Suppose that we have a cube with sidelength M.

if we rescale this measure with a scale factor 8, we get 8*M

Now, if previously the area of one side was of order M^2, with the rescaled measure the area will be something like (8*M)^2 = 64*M^2

This means that the ratio of the surfaces/areas will be 64.

(and will be the same for a pyramid, a rectangle, etc)

Then the correct options will be the ones related to surfaces, that are:

The scaled surface area of a square pyramid to the original surface area.

The scaled area of a triangle to the original area.

5 0
3 years ago
Can someone help me find the area of the following figure
ExtremeBDS [4]
1. The area of the full rectangle is 21 * 28 = 588. We will need this later. 

Like you drew, there is an imaginary triangle missing. We can find the dimensions of it by subtracting from the given information. The shorter leg of it is 21 - 12 = 9, the longer leg is 28 - 14 = 14.

Now we find the area of the triangle. Area of a triangle is 1/2 * base * height. So 1/2 * 9 * 14 = 1/2 * 126 = 63. 

Now we do the full area of 588 minus the area of the missing triangle piece. 

588 - 63 = 525 ft²

2. Do the area of the rectangle and then this time add on the area of the triangle. 7 * 15 = 105. Area of the triangle = 1/2 * 2 * 7 = 1/2 * 14 = 7. 

105 + 7 = 112 in²
6 0
3 years ago
Other questions:
  • A side of a regular six - sided polygon is 8cm long. The perimeter of a similar polygon is 60cm. What is the length of a side of
    12·1 answer
  • How to divided big numbers using super seven
    8·1 answer
  • 24% of 1321 is how much? round the answer to the nearest hundredth
    5·2 answers
  • You throw a dart at the board shown. Your dart is equally likely to hit any point inside the square board. Find the probability
    10·1 answer
  • Solve by graphing. Round each answer to the nearest tenth.<br><br> 6x^2 + 31x = 12
    6·1 answer
  • Angela got a new job that pays $24.25 per hour she works 40 hours per week she pays 5% state income tax on her earnings how much
    12·1 answer
  • Lucy invested $19,000 in an account paying an interest rate of 3% compounded annually. Assuming no deposits or withdrawals are m
    15·1 answer
  • Joy’s garden produced 447 green beans. Sammy’s garden produced 392 green beans. About how many green beans did Joy and Sammy’s g
    7·2 answers
  • Rewrite the expression by factoring out (w-2).<br> 5w(w – 2) + 2(w-2)
    9·1 answer
  • ASAP,What are the possible solutions to a system of equations and What does it mean for a system of equations to have one Soluti
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!