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
Judd is 3 years older than Jordan. Jordan is 6 years younger than Chris. Write an algebraic expression for the sum of their ages
Cloud [144]

Answer:

تيتلتبنبزلمينبووبصحثنل

6 0
2 years ago
A. 55<br> b. 70<br> c. 110<br> d. 125
morpeh [17]

Answer:

b

Step-by-step explanation:

7 0
2 years ago
Simplify: x2/6 ⋅ x2/4
Elden [556K]

Answer:

x ^2/ 6

--------------------------------------------------------------------------

8 0
3 years ago
Type your answer in the box. <br><br> y = 10 b = 6
blondinia [14]

Answer:

The answer is -60 (I believe)

Step-by-step explanation:

3(-10)-5(6)

-30-30 = -30+-30

-30+-30= -60

The answer is -60

6 0
2 years ago
Read 2 more answers
What integers are closet to the number 95
astraxan [27]

Answer:

94 and 96

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Other questions:
  • Please help me with this ty so much
    10·1 answer
  • Pleaseee help I’m struggling so hard
    14·2 answers
  • Help With A Question
    13·1 answer
  • Derrico is building a holding pen for his dogs. The rectangular holding pen is 14.8 feet wide by 8.9 feet long. About how many f
    6·2 answers
  • Give the function f(x) = x + 7<br>find f(5)​
    15·1 answer
  • Rebecca supplies costumes to a number of theater companies and recently lent out a number of different hats. turbans 6 berets 3
    12·1 answer
  • What is the surface area of a right circular cylinder with a diameter of 14 meters and a height of 9 meters
    12·1 answer
  • SOMEONE PLEASE HELP ME! I promise i will mark brainlest, but i need the right answer for this. help is much appreciated &lt;3
    15·2 answers
  • Find the slope of x+2/3
    6·2 answers
  • a model of a car is amde to a scale of 1:40. the volume of the model is 45cm^3. calcualte the volume of the car. give your answe
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!