# Confidence Interval and Standard Deviation

• May 17th 2009, 03:30 AM
Phil32686
Confidence Interval and Standard Deviation

ABC College Bookstore sells Ti83 calculators. The random number of calculators sold per day along with the probabilities is:

# of calculators: 1, 2, 3, 4, 5
Probability: 1/8, 1/6, 1/2, 1/12, 1/8

What is the standard deviation for the number of calculators sold?

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Find a 95% confidence interval for the mean weight of bass caught in El Capitan lake if a sample of 300 fish had a mean weight of 77 ozs. with a standard deviation of 12 ozs.

I've been trying to figure these out for a while and still can't get it right. :(
• May 17th 2009, 05:42 AM
mr fantastic
Quote:

Originally Posted by Phil32686

ABC College Bookstore sells Ti83 calculators. The random number of calculators sold per day along with the probabilities is:

# of calculators: 1, 2, 3, 4, 5
Probability: 1/8, 1/6, 1/2, 1/12, 1/8

What is the standard deviation for the number of calculators sold?

---

Find a 95% confidence interval for the mean weight of bass caught in El Capitan lake if a sample of 300 fish had a mean weight of 77 ozs. with a standard deviation of 12 ozs.

I've been trying to figure these out for a while and still can't get it right. :(

Q1 Use \$\displaystyle Var(X) = E(X^2) - [E(X)]^2\$. If you need more help, please show your working and say where you get stuck.

You will find many questions on confidence intervals (with helpful replies) at MHF by using the Search tool (top right).
• May 17th 2009, 12:41 PM
Phil32686
Quote:

Originally Posted by mr fantastic
Q1 Use \$\displaystyle Var(X) = E(X^2) - [E(X)]^2\$. If you need more help, please show your working and say where you get stuck.

You will find many questions on confidence intervals (with helpful replies) at MHF by using the Search tool (top right).

For the first one, would I plug in probability for E and # of calculators for X?

= (1/8)(1^2) - [(1/8*1)^2] + etc...

And do that for all of the # of calculators and probabilities for each?

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For the Confidence Interval question, I got

75.6421 < u < 78.3579
• May 17th 2009, 08:15 PM
mr fantastic
Quote:

Originally Posted by Phil32686
For the first one, would I plug in probability for E and # of calculators for X?

= (1/8)(1^2) - [(1/8*1)^2] + etc...

And do that for all of the # of calculators and probabilities for each?

[snip]

You calculate these things using the usual definitions:

E(X) = (1)(1/8) + (2)(1/6) + ....

E(X^2) = (1^2) (1/8) + (2^2) (1/6) + ....