A community for students.
Here's the question you clicked on:
 0 viewing
xEnOnn
 3 years ago
A population of normally distributed account balances have mean balance $150 and standard deviation of $35. What is the probability that the total balance for a random sample of 40 accounts will exceed $6400?
xEnOnn
 3 years ago
A population of normally distributed account balances have mean balance $150 and standard deviation of $35. What is the probability that the total balance for a random sample of 40 accounts will exceed $6400?

This Question is Closed

campbell_st
 3 years ago
Best ResponseYou've already chosen the best response.1find the average balance for the 40... 6400/40 = $160 this means that the average balance of the 40 selected exceeds $160

DBhatta
 3 years ago
Best ResponseYou've already chosen the best response.2X~N(150,35) X= Total balance / 40 X= 6400/40 X = 160 P(X>160) = ? =P(Z>(1600150)/35) =P(Z>0.285) = 1 P(z<0.285) =1  0.6122 = 0.3878

campbell_st
 3 years ago
Best ResponseYou've already chosen the best response.1using a z score \[z =(x  \mu)/\sigma\] \[z = (160  150)/35\] z = 0.2857

xEnOnn
 3 years ago
Best ResponseYou've already chosen the best response.1Thanks! hmm...actually, I have also calculated both the different answers by @DBhatta and @campbell_st. And that's why I am not sure what the correct answer should be. hahaha...

campbell_st
 3 years ago
Best ResponseYou've already chosen the best response.1I would have thought that if the balance is to exceed then its the probability should be between 50% and 68%... as the average is greater than the mean... and the z score is 0.2857

DBhatta
 3 years ago
Best ResponseYou've already chosen the best response.2I'm pretty sure with my answer and @campbell_st also has the same answer. He has just stopped after calculating z and I've calculated until the end.

DBhatta
 3 years ago
Best ResponseYou've already chosen the best response.2@campbell_st actually it should be below 50% dw:1335172829891:dw

xEnOnn
 3 years ago
Best ResponseYou've already chosen the best response.1oh no...wait, so sorry, I saw the wrong numbers. Yes, @campbell_st and $DBhatta both has the same answer. Actually, here's what I got for my other answer: \[\frac { 160150 }{ \frac { 35 }{ \sqrt { 40 } } } =1.807\]

xEnOnn
 3 years ago
Best ResponseYou've already chosen the best response.1I don't know which is the right way to look at this problem.

campbell_st
 3 years ago
Best ResponseYou've already chosen the best response.1DBhatta's graph sums it up

DBhatta
 3 years ago
Best ResponseYou've already chosen the best response.2@xEnOnn are you using z test or normal distribution? The question asks about normal distribution.

xEnOnn
 3 years ago
Best ResponseYou've already chosen the best response.1oh, is what I have done a ztest instead of a normal distribution?

DBhatta
 3 years ago
Best ResponseYou've already chosen the best response.2yes my friend. It should be normal distribution \[z = x  u / \sigma \]

xEnOnn
 3 years ago
Best ResponseYou've already chosen the best response.1But it has that 40 accounts info, isn't that n=40?

DBhatta
 3 years ago
Best ResponseYou've already chosen the best response.2ah...let me see. it's becoming more interesting now.

DBhatta
 3 years ago
Best ResponseYou've already chosen the best response.2oh yes, it's zdistribution.

xEnOnn
 3 years ago
Best ResponseYou've already chosen the best response.1oh so we should use the other method? The one I written just now? But why?

DBhatta
 3 years ago
Best ResponseYou've already chosen the best response.2Yes use the one you have written. We are assuming that population mean is equal to the sample mean.

xEnOnn
 3 years ago
Best ResponseYou've already chosen the best response.1oh I see...Thanks for you help!! :)

DBhatta
 3 years ago
Best ResponseYou've already chosen the best response.2Actually you helped me, I was offtrack. It was you who made me realize. :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.