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]
2 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]2 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
The Midpoint of GH is M(4,-3). One endpoint is G(-2,2). Find the coordinates of endpoint H.
77julia77 [94]

Answer:

Step-by-step explanation:

(x - 2)/2 = 4

x - 2 = 8

x = 10

(y + 2)/2 = -3

y + 2 = -6

y = -8

(10, -8)

3 0
3 years ago
Simplify 8(3+5)<br><br><br> Help me please
amid [387]

Answer:

64

Step-by-step explanation:

pemdas says parenthesis first

3+5=8

8(8)

8 times 8 equals 64

3 0
3 years ago
Read 2 more answers
write an equation of a line that passes through the following tow points (4, -6) and (2, 8) show work
stiks02 [169]

Answer:

y = -7x + 22

Step-by-step explanation:

Given

(x_1,y_1) = (4,-6)

(x_2,y_2) = (2,8)

Required

Determine the line equation

This question will be answered using linear interpolation.

This is represented as thus:

\frac{y - y_1}{x - x_1} = \frac{y_2 - y_1}{x_2 - x_1}

Substitute values for x1,x2,y1 and y2

\frac{y - (-6)}{x - 4} = \frac{8 - (-6)}{2 - 4}

\frac{y +6}{x - 4} = \frac{8 +6}{2 - 4}

\frac{y +6}{x - 4} = \frac{14}{-2}

\frac{y +6}{x - 4} =-7

Cross Multiply

y + 6 = -7(x - 4)

y + 6 = -7x + 28

Make y the subject

y = -7x + 28-6

y = -7x + 22

7 0
3 years ago
Which is better for music SteelSeries arcits pro wireless vs v-moda crossfade wireless
LUCKY_DIMON [66]

Answer:

SteelSeries arcits pro wireless

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Use the given information to bound the p-value of the F statistic for a one-tailed test with the indicated degrees of freedom. F
lianna [129]

Answer:

The range of the <em>p</em>-value is: 0.050 < <em>p</em>-value < 0.100.

Step-by-step explanation:

For checking the equivalence of two population variances of independent samples, we use the <em>f</em>-test.

The test statistic is given by:

F=\frac{S_{1}^{2}}{S_{2}^{2}}\sim F_{\alpha, (n_{1}-1)(n_{2}-1)}

It is provided that the hypothesis test is one-tailed.

The computed value of the test statistic is:

<em>F</em> = 4.23.

The degrees of freedom of the numerator and denominator are:

df_{1}=4\\df_{2}=5

Use MS-Excel to compute the <em>p</em>-value as follows:

Step 1: Select function fX → F.DIST.RT.

Step 2: A dialog box will open. Enter the values of f-statistic and the two degrees of freedom.

*See the attachment below.

Step 3: Press OK.

The <em>p</em>-value is, 0.0728.

The range of the <em>p</em>-value is:

0.050 < <em>p</em>-value < 0.100

4 0
3 years ago
Other questions:
  • For what values of x does the binomial 2x−1 take on a positive value?
    7·1 answer
  • What is the result of 36 divided by 9? Use the number line to find the answer. A number line going from 0 to 39. The numbers 0,
    11·2 answers
  • HELP ME PLZZZZZZZ WHICH OF THE FOLLOWING STATEMENT <br> S ABOUT RATIONAL NUMBERS IS NOT CORRECT
    12·1 answer
  • Uadrilateral ABCD has coordinates A (3, 1), B (4, 4), C (7, 5), D (6, 2). Quadrilateral ABCD is a
    8·1 answer
  • Nia built the following graph to model a probe flying close to Mars and then on to outer space. Which of the following domains i
    12·1 answer
  • Find the circumference of a circle thats diameter is 6 m
    13·2 answers
  • Given that y^x=x^y, wich of the following expressions equal dy/dx?
    11·2 answers
  • triangle abc is graphed on a coordinate plane, as shown below. Triangle ABC is dilated by a scale factor of 2 with a center of d
    9·1 answer
  • a woodworker wants to cut a board that is 8.225 feet long into 5 equal pieces. How long will each of the boards be?​
    12·2 answers
  • Explain how you know that 88 is a solution to the equation 18x=11 by completing the sentences: The word "solution" means . . . 8
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!