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
Nadia charges $7.00 an hour for babysitting. She babysits 19.50 hours the first week of the month and 19 hours the second week o
Alekssandra [29.7K]

Answer:

35

Step-by-step explanation:

19+19.50=38.5

38.5×7=269.5

269.5÷7.70=35

4 0
3 years ago
What's -5√3(2+√5)?<br><br><br> h e l p .
riadik2000 [5.3K]
Here you go hope it helps

6 0
3 years ago
Read 2 more answers
PLEASE BE RIGHT AND SOLVE
Sergeeva-Olga [200]

Answer:

Option B: Rotation

Step-by-step explanation:

The shape appears to have the same size, but it has been moved in a way that  is not reflection. Through the process of elimination, the answer is rotation.

4 0
3 years ago
Read 2 more answers
At the market, 2.4 pounds of peas cost 1.68 dollars. How much does one pound of peas cost?
babunello [35]
.7

because you need to get the original unit price which is 0.7 then multiply that by 1 and get your answer
6 0
4 years ago
Find the equation of the
kolbaska11 [484]

Answer:

y=-1/3 x +2/3

Step-by-step explanation:

all steps are in picture

4 0
3 years ago
Other questions:
  • Look at the following number sequence.
    10·1 answer
  • What is the median of 4,17,17,4,27,29,20,24,34,4
    5·1 answer
  • Maggie‘s brother is 11 years younger than four times her age. The sum of their ages is 54. How old is Maggie?
    14·1 answer
  • On a recent survey, 40 percent of those surveyed indicated that they prefer lemonade or sweet tea. If 720 people preferred lemon
    15·1 answer
  • A reading list contains 3 historical books and 4 science-fiction books. What is the probability that Tena will randomly choose a
    13·1 answer
  • Last question on this site if anyone wanna help
    10·1 answer
  • What is 288889 divide by 676767 please help
    9·2 answers
  • What are the coordinates of each point after quadrilateral ABCD is reflected across the y-axis and then translated 2 units down?
    10·1 answer
  • !!!! HELP!!! BRAINLIEST !!!!What is the value of x?<br> Enter your answer in the box.<br> X=
    13·2 answers
  • What is the reciprocal of the divisor 3/ 2 ​ ÷ 5 /6?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!