Using the normal distribution, it is found that there is a 0.963 = 96.3% probability that on a given day, his commute will be longer than 49 minutes.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean
and standard deviation
is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
In this problem, the mean and the standard deviation are given, respectively, by:
.
The probability that on a given day, his commute will be longer than 49 minutes is <u>one subtracted by the p-value of Z when X = 49</u>, hence:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{49 - 57}{4.5}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B49%20-%2057%7D%7B4.5%7D)
Z = -1.78
Z = -1.78 has a p-value of 0.0375.
1 - 0.0375 = 0.963.
0.963 = 96.3% probability that on a given day, his commute will be longer than 49 minutes.
More can be learned about the normal distribution at brainly.com/question/24663213
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Answer:
Reading and writing skills, writing essays, mathematics, and English as a second language.
Explanation:
COMPASS is a computer-based assessment tool that evaluates different students' skills: reading and writing, writing essays, math, and English as a second language. Thanks to the results and information provided by this program, professors can determine what courses would suit the students and help them access all needed resources in order to reach their full potential.
Answer:
FDR was an American politician and attorney who served as the 32nd President of the United States from 1933 to 1945.
Executive Order 9066, signed by President Franklin D. Roosevelt on February 19, 1942, gave the secretary of war and his commanders the authority to "prescribe military areas in such places and to such extent as he or the appropriate Military Commander may determine, from which any or all persons may be excluded."
Explanation:
Answer:
How many times can you subtract 10 from 100?
Explanation:
Once. The next time you would be subtracting 10 from 90.
Let x = the number
.05 = .1x
5/100 = (1/10)x Multiply both sides by 10.
5/10 = x
1/2 = x