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Probability - Amount of money in pocket

mathmari

Well-known member
MHB Site Helper
Apr 14, 2013
4,693
Hey!! :giggle:

The amount of money a student in the Accounting Department has in his pocket is a random variable that follows the normal distribution, with an average price of $30$ euros and a variance of $100$.

a) What is the probability that a student has $25$ to $35$ euros in his pocket?

b) If we randomly select $25$ students, then what is the probability that a student has less than $20$ euros in his pocket?

c) How much money does $75\%$ of students have in their pocket?



I have done the following :

a) We have that the standard deviation is equal to $\sqrt{100}=10$.

Do we have to use the $z$-score?

We have that $Z=\frac{X-\mu}{\sigma}=\frac{X-30}{10}$.
Then \begin{align*}P(25\leq X\leq 35)&=P(X\leq 35)-P(X\leq 25)\\ & =P\left (Z\leq \frac{35-30}{10}\right )-P\left (Z\leq \frac{25-30}{10}\right )\\ & =P\left (Z\leq 0.5\right )-P\left (Z\leq 0.5\right )\end{align*} Is that correct so far?


b) Could you give me a hint?

:unsure:
 

romsek

New member
Mar 27, 2017
17
a) read your text

b) given a set of independent Gaussian random variables what is the distribution of their sum? Don't know? Read your text.
Once you've established that the problem is the similar to (a)

c) Use the inverse of the CDF of the standard normal to find the z-score of 0.75. Convert the z-score into how much money using the mean and standard deviation as usual.
 

Prove It

Well-known member
MHB Math Helper
Jan 26, 2012
1,453
Are you allowed to use technology?