Probability - Amount of money in pocket

• MHB
• mathmari
In summary: 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.Are you allowed to use technology?I always considered paper and pencil "technology". They don't grow on trees!I always considered paper and pencil "technology". They don't grow on trees!
mathmari
Gold Member
MHB
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:

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.

Are you allowed to use technology?

I always considered paper and pencil "technology". They don't grow on trees!

Country Boy said:
I always considered paper and pencil "technology". They don't grow on trees!

Last time I checked, both paper and pencils do in fact come from trees...

But I digress, either the OP will need to use a calculator with a Normal Probability function on it to get the values, or else refer to a normal table. That is why I asked...

Yes, "come from trees". Buy I said "grow on trees". I takes technology to convert trees to paper and pencils!

mathmari said:
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 $35$ uueuros 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?
This seems to me to be ambiguous. Does it mean "at least one of the 25 students is less than 20 euros" or "all 25 have less than 20 Euros"?

c) How much money does $75\%$ of students have in their pocket?
Also ambiguous- the total of 75% of the students? And which 75%? It might be intended that 75% of the students have the same amount and that is what is being asked.

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:

1. What is probability?

Probability is a mathematical concept that measures the likelihood of an event occurring. It is represented as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.

2. How is probability related to the amount of money in my pocket?

The probability of the amount of money in your pocket is the likelihood of randomly selecting a specific amount of money from your pocket. For example, if you have $10 in your pocket and$50 in your wallet, the probability of randomly selecting $10 from your pocket is higher than randomly selecting$50.

3. How can I calculate the probability of a specific amount of money in my pocket?

To calculate the probability of a specific amount of money in your pocket, you need to know the total amount of money in your pocket and the amount you are interested in. The probability can be calculated by dividing the amount you are interested in by the total amount of money in your pocket.

4. What factors can affect the probability of a specific amount of money in my pocket?

The probability of a specific amount of money in your pocket can be affected by various factors, such as the amount of money you usually carry, your spending habits, and any recent purchases or withdrawals. It can also be influenced by external factors, such as winning a lottery or receiving a gift.

5. How can understanding probability help me manage my finances?

Understanding probability can help you make informed decisions about your finances. By understanding the likelihood of certain events, such as winning a lottery or losing money in a bet, you can make better financial choices and manage your money more effectively.

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