Sampling and Normal Distribution

1) A Problem of N=10000 has Sigma=25. In each of the following cases, which formula will you use to calculate the standard deviation of the sample mean and then use the appropriate formula to calculate it:
a. n=2000 b. n=300

 

4) A machine that cuts and wraps cheese is supposed to produce packages the contain 10 oz of cheeese. Due to variabilty in the process the actual amount of cheese varies slighty. The amount of cheese cut and packaged in this manner follows a normal distribution with a mean than can be set to any desired value. The standard deviation of the amount of cheese is always 0.1-oz, regardless of the mean of the amount. If the company wants to make sure than 99% of the packages contain at least 10-oz of cheese, to what value should the mean of the machine be set?

 

5) Suppose the incomes of all people in America who own hybrid vehicles are distributed with a mean of $58,000 and a standard deviation of $8300. Let x-bar be the mean income of a random sample of 50 such owners . Determine the mean and standard deviation of the sampling distribution and describe its shape. Calculate the probability that the mean of such a sample would be greater than $60,000.

 

6)Brooklyn Corps manufactures CDs. The machine that is used to make these CDs is known to produce 6% defective CDs. The quality control inspector selects a sample of 100 CDs randomly every day and inspects them for being good of defective. if 8% or more of the CD’s in the sample are defective, the process is stopped and the machine is readjusted. What is the probability that based on sample of 100 CDs the process will be stopped to readjust the machine, if the true percentage is 6%? what is the mean and standard deviation and shape of the sampling distribution for p-hat?

 

7. The distance from a college to a students home follows a right skewed distribution with a mean if 15 miles and a standard deviation of 8 miles.

a. find the probability that the mean distance from college to a students home for a random sample of 50 college students is more than 18 miles

b. for this sample of 50 students, find the probability that their distance from college to home is between 14 & 17 miles.

c. What is the shape of the sampling distribution if a random sample of 10 students was selected instead of 50? can you determine the mean or standard deviation of this new sampling distribution? if so what are they? if not, why not?

 

3. Freddy is taking Basic Stats class. The class starts at 6 pm and he needs to get there on time to get a punctuality bonus point. Freddy leaves from home and at that time of day i takes him an average of 15 min to get to the classroom. However, due to variability in traffic and parking conditions, the standard deviation of his srips is 3 mins. Suppose the population of his time to reach the classroom has a normal distribution of with a mean of 15 min and a standard deviation of 3 min.
a. what time should Freddy leave home for class so that he gets the bonus point 99% of the time
b. If he leaves at 5:40 pm. what percentage of the time would he get the bonus point
please show work, so I can also understand the steps!