Math 116 Essay

Assume that X is a binomial random variable with n = 27 and p = 0.92. Calculate the following probabilities. (Round your intermediate and final answers to 4 decimal places.)

Pg 212 #14) A normal population has a mean of 12.2 and a standard deviation of 2.5.

D) The probability of 70 or more correct guesses if the subject is guessing at the chance rate.

9. Flip a coin 25 times and keep track of the results. What is the experimental probability of landing on tails? What is the theoretical probability of landing on heads or tails?

This is an important problem and is addressed by the Central Limit Theorem. For now, let us not bother about what this theorem states but we will look at how it could help us in answering our question.

21) Seventy two percent of all observations fall within 1 standard deviation of the mean if the data is normally distributed.

A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces. Suppose that in a particular of 50 packages, the mean amount dispensed is 8.159 ounces, with a sample standard deviation of 0.051

Ref: CQI Study Guide Q13 21. In a normal curve, approximately what percentage of the area is included within 3 standard deviations of the mean? a. 50.0% b. 66.6% c. 95.0% Page 4 of 32

3) No, the ages are not normally distributed because with the view of the histogram, it is not bell shaped.

At a computer manufacturing company, the actual size of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A random sample of 12 computer chips is taken. Above what value do 2.5% of the sample means fall? ANSWER: 1.057

of the last 220 applicants 14 failed the test. Develop a 99% confidence interval for the proprotion of applicants that fail the test. Would it be reasonable to conclude that more than 10% of the apllicants are now failing the test? In addition to the testing of applicants, fashion industries randomly tests its employees throughout the year. Last year in the 400 random tests conducted, 14 employees failed the test. Would it be reasonable to conclude that less than 5% of the employees are not able to pass the random drug test?

These past few weeks we have covered the central tendency, variability, correlation and now we will look at something that has a correlation with standard deviation and mean. I hope you still remember the bell shape of the standard deviation graph! That is ok, if you do not. I will briefly do my best to summarize it. The Standard Deviation (SD) is the average distance from the mean. In a normal distribution, the standard deviation is the standard that is 34 % of the cases to the right that would be one positive standard deviation and 34% to the left and that would be one negative SD. Majority of the data will be between -3 and +3 standard deviation from the mean; which is applicable to all normal

17. The probabilities of the events A and B are .20 and.30, respectively. The probability that

The Normal distribution or Gaussian distribution is an average distribution of values that resemble the shape of a bell which is symmetric about the mean. Most of the values in a normal distribution fall near the average with less values falling behind it. It is produced when the number of data points is relatively large. The curve formed by a normal distribution is called a normal curve or bell curve. If the values are precise, the curve is tall and thin while unprecise data gives a short and wide normal curve.

Whether it be using Grey’s Anatomy watching habits, dog walking habits, or the pitch of a dog bark, the Central Limit Theorem can turn a binomial graph into a normal graph. This can be easily done by taking a random sample of over 30 from the data given, taking the means from each sample, and then plotting them on a graph will give us an approximately normal