# Thread: another question

1. ## another question

a) Profits (denoted as X) 100 normally distributed mean value of 1.5 mi and a (s.d.) of 120,000.

Calculate P (X < $1 million) 2. Originally Posted by crashuk a) Profits (denoted as X) in an industry consisting of 100 firms are normally distributed with a mean value of$1.5 million and a standard deviation (s.d.) of $120,000. Calculate P (X <$1 million)
Pr(Z < -4.1667).

Your tables will give zero as the answer. Which is correct, to four decimal places.

3. any chance of explaining it please

4. so would it be 1M-1.5M/120,000 is that how you did it.

5. Originally Posted by crashuk
so would it be 1M-1.5M/120,000 is that how you did it.
That's how I got the z-value, yes.

6. Suppose a random sample of 10 firms gave a mean profit of $900,000 and a (sample) standard deviation of$100,000.

so i do the same steps as the rest?
so here i would use T as the random sample of 10 is under 30, 30 and over i use z system and for T 29 and less . is that correct?

7. Originally Posted by crashuk
Suppose a random sample of 10 firms gave a mean profit of $900,000 and a (sample) standard deviation of$100,000.

so i do the same steps as the rest?
This one will probably be different. What does the question ask you to do?

8. Suppose a random sample of 10 firms gave a mean profit of $900,000 and a (sample) standard deviation of$100,000. Establish a 95% confidence interval for the true mean profit in the industry. Which probability distribution do you use? Why?

9. Originally Posted by crashuk
Suppose a random sample of 10 firms gave a mean profit of $900,000 and a (sample) standard deviation of$100,000. Establish a 95% confidence interval for the true mean profit in the industry. Which probability distribution do you use? Why?
Use the t-distribution because the population sd is unknown. Although n is small (n < 30), from your previous question it's known that the data comes from a normal population so using the t-distribution is OK.

As for the confidence interval, you will find the necessary formulae at this thread: http://www.mathhelpforum.com/math-he...intervals.html

### profits (x) in an industry consisting of 100 firms are normally distributed with a mean value of 1.5 million and a standard deviation of 120,000

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