# Normal Distribution (Prob something will be EXACT?)

• Apr 23rd 2009, 08:14 PM
rikkoo
Normal Distribution (Prob something will be EXACT?)
Suppose x ~ N ($1400,$200^2) | Sales if soft drinks for a movie theater

a.) What percentage of sales are above $1450 for the week? Is this correct?: P (x>1450) = p(z > (1450-1400)/200 = p(z > .25) = p(z < -.25) = .4013 = 40.13% b) What is the probability sales will be EXACTLY$1200?

c) How much money must be made for sales to perform in top 5%?
• Apr 23rd 2009, 09:07 PM
pickslides
Quote:

Originally Posted by rikkoo
Suppose x ~ N ($1400,$200^2) | Sales if soft drinks for a movie theater

a.) What percentage of sales are above $1450 for the week? Is this correct?: P (x>1450) = p(z > (1450-1400)/200 = p(z > .25) = p(z < -.25) = .4013 = 40.13% b) What is the probability sales will be EXACTLY$1200?

c) How much money must be made for sales to perform in top 5%?

hi there, try the same for b) as you did in a) except use

$\displaystyle P (x=1200) \Rightarrow P(z = \frac{200-1400}{200})$

for part c)

$\displaystyle P (x=A) = .95 \Rightarrow A = 1.65$

from standard normal dist table, then

$\displaystyle \frac{x-1400}{200} = 1.65$

then solve for x
• Apr 25th 2009, 07:19 PM
rikkoo
I thought zero will be the area. Thanks! What about a problem like this:

2.) A friend of yours works as an employee at your favorite restaurant. He or she keeps track of how many hamburgers are ordered in a day. He or she tells you that the number of hamburgers ordered in a day is normally distributed with a mean of 45 and a standard deviation of 8.4.

a.) What is the probability distribution (type of distribution, mean and standard deviation) of the average hamburgers ordered for 50 customers? 100 customers? 1000 customers?

b.) What happens to the standard deviation of the sample mean? Is it better to sample more or less customers and why?

c.) What is the probability that the sample average orders of hamburgers is greater than 55 for 100 customers?

Also need help with this:

3.) The local newspaper reports that the population proportion of college students that attend every class all semester is 0.15.

a.) Show the sampling distribution of the sample proportion if 300 students are sampled.

b.) Is it appropriate to use a normal distribution to approximate the distribution of the sample proportion? Why or why not?

c.) What is the probability that out of 100 students sampled the proportion of those attending every class is between 0.1 and 0.3?
• Apr 25th 2009, 07:26 PM
The Second Solution
Quote:

Originally Posted by rikkoo
I thought zero will be the area. Thanks! What about a problem like this:

2.) A friend of yours works as an employee at your favorite restaurant. He or she keeps track of how many hamburgers are ordered in a day. He or she tells you that the number of hamburgers ordered in a day is normally distributed with a mean of 45 and a standard deviation of 8.4.

a.) What is the probability distribution (type of distribution, mean and standard deviation) of the average hamburgers ordered for 50 customers? 100 customers? 1000 customers?

b.) What happens to the standard deviation of the sample mean? Is it better to sample more or less customers and why?

c.) What is the probability that the sample average orders of hamburgers is greater than 55 for 100 customers?

Also need help with this:

3.) The local newspaper reports that the population proportion of college students that attend every class all semester is 0.15.

a.) Show the sampling distribution of the sample proportion if 300 students are sampled.

b.) Is it appropriate to use a normal distribution to approximate the distribution of the sample proportion? Why or why not?

c.) What is the probability that out of 100 students sampled the proportion of those attending every class is between 0.1 and 0.3?

Q2 was asked at http://www.mathhelpforum.com/math-he...tribution.html and my same comment applies.
• Apr 25th 2009, 07:35 PM
rikkoo
I don't get it either. Odd question. Do we replace the original mean given in the problem?