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
postnew [5]
3 years ago
8

I arrive at a bus stop at a time that is normally distributed with mean 08:00 and SD 2 minutes. My bus arrives at the stop at an

independent normally distributed time with mean 08:05 a.m. and SD 3 minutes. The bus remains at the stop for 1 minute and then leaves. What is the chance that I miss the bus
Mathematics
1 answer:
Nimfa-mama [501]3 years ago
5 0

Answer:

0.0485 = 4.85% probability that you miss the bus.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

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

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.

When two normal distributions are subtracted, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.

In this question:

We have to find the distribution for the difference in times between when you arrive and when the bus arrives.

You arrive at 8, so we consider the mean 0. The bus arrives at 8:05, 5 minutes later, so we consider mean 5. This means that the mean is:

\mu = 0 - 5 = -5

The standard deviation of your arrival time is of 2 minutes, while for the bus it is 3. So

\sigma = \sqrt{2^2 + 3^2} = \sqrt{13}

The bus remains at the stop for 1 minute and then leaves. What is the chance that I miss the bus?

You will miss the bus if the difference is larger than 1. So this probability is 1 subtracted by the pvalue of Z when X = 1.

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

Z = \frac{1 - (-5)}{\sqrt{13}}

Z = \frac{6}{\sqrt{13}}

Z = 1.66

Z = 1.66 has a pvalue of 0.9515

1 - 0.9515 = 0.0485

0.0485 = 4.85% probability that you miss the bus.

You might be interested in
0.79 x 3.7 =<br> please explain your process
mart [117]

This question is super easy.

0.79*3.7

=2.923

Hope this helps!

Thanks!

-Charlie

3 0
3 years ago
Help i'll make you the brainliest
9966 [12]

Answer:

D) b = \frac{S-2ac}{2a + 2c}

Step-by-step explanation:

First, move all the terms that do not include b to the left side with S:

S = 2ab + 2bc + 2ac

S - 2ac = 2ab + 2bc

Now, factor out 2b from the right side:

S - 2ac = 2b(a + c)

Divide both sides by 2(a + c):

b = \frac{S-2ac}{2(a + c)}

Finally, multiply out the denominator:

b = \frac{S-2ac}{2a + 2c}

7 0
3 years ago
Which system of equations has the same solution as the system below?
worty [1.4K]

Answer: Both A, and C

Step-by-step explanation:

The answer to the first system of equations (2x+2y=16) would be

x=3 and y=5 ( 3x-y=4 )

Which means we have to find out which of the other equations has an x value of 3, and a y value of 5.

If A is 2x+2y=16, then x=3 and y=5

           6x-2y=8

If B is x+y=16, then x=5 and y=11

         3x-y=4

If C is 2x+2y=16, then x=3 and y=5

           6x-2y=8

If D is 6x+6y=48 , then x=-2 and y=10

            6x+2y=8

Both A and C are equal to the first system of equations, which means they are both correct answers.

8 0
3 years ago
Which inequality represents all values of X for which the product below is defined
balandron [24]

The domain for which the function is defined is given by:

D. x \geq 4.

<h3>What is the domain of a function?</h3>

The domain of a function is the set that contains all possible input values for the function.

A square root is only defined for non-negative values, hence:

  • x - 4 \geq 0 \rightarrow x \geq 4.
  • x + 1 \geq 0 \rightarrow x \geq -1.

The intersection of these two domains is x \geq 4, hence option D is correct.

More can be learned about the domain of a function at brainly.com/question/10891721

#SPJ1

6 0
2 years ago
Lucy has block letters that are in the shape of cubes with sides 2 3 foot long. She has a box which is 1 1 3 foot long, 2 3 foot
MrMuchimi

Complete question :

Lucy has block letters that are in the shape of cubes with sides 2 3 foot long. She has a box which is 1 1 3 foot long, 2 3 foot wide, and 2 3 foot tall. Find the number of block letters that will fit in the box.

Answer:

1/2

Step-by-step explanation:

Number of block letters that will fit in :

Volume of box ÷ volume of each letter cube

Volume of each letter cube = (side length)³ = (2/3)³ = 8/27 ft³

Volume of box = length * width * height

Volume of box = 1 1/3 * 2/3 * 2/3

Volume of box = 4/3 * 2/3 * 2/3 = 16 / 27 ft³

Therefore ;

8/27 ÷ 16/27

8/27 * 27/16

= 8/16

= 1/2

7 0
3 years ago
Other questions:
  • What is 1036.50 rounded the the nearest whole number?
    14·1 answer
  • What are the solutions of the equation? 0=x^2-2x-24
    7·1 answer
  • A triangle has a base that measures 6.4 feet. It’s height measures 5 feet. How many square feet is the area of the triangle?
    14·1 answer
  • Simplify<br> 4-3[6-2(4-3)]
    13·1 answer
  • A New York Times/CBS poll surveyed 1,027 adults nationwide about race relations in the United States. Of the sample, 61% respond
    8·1 answer
  • Solve equation and show all steps what is 3/8x=36
    11·2 answers
  • BRAINLIEST GUARANTEED. Please Answer and show work. I'm not sure if it's correct though.
    5·2 answers
  • Find the gradient of y=x³ + 6, using the
    6·1 answer
  • 1. K + 8 &gt; 19, if k = 11 is this a true statement
    8·1 answer
  • I do not understand how to solve this problem I would appreciate it if someone could help me
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!