Overview

This is a fun assignment to do. In chapter 5 you learned about basic probability and learned about conditional probability. Now, you get to see these two in action. You may have heard of the TV game: Let’s make a Deal. Where at the end of the show, contestants are presented with 3 doors and they are informed that behind one of the doors is a brand new card. So, the contestant chooses one of three doors. Then the game show host (First one was Monty Hall), opens a door and reveals a goat. Then Monty asks if the contestant wants to switch or not. So the question is, what is the probability of winning? Should I stay, or should I switch? What would you do?

Instructions

Imagine that the set of Monty Hall’s game show Let’s Make a Deal has three closed doors. Behind one of these doors is a car; behind the other two are goats. The contestant does not know where the car is, but Monty Hall does. The contestant picks a door and Monty opens one of the remaining doors, one he knows doesn’t hide the car. If the contestant has already chosen the correct door, Monty is equally likely to open either of the two remaining doors. After Monty has shown a goat behind the door that he opens, the contestant is always given the option to switch doors. What is the probability of winning the car if she stays with her first choice? What if she decides to switch? Think about what you think the answer is: stay or switch?

1. Watch a YouTube video that explains the problem: “Monty Hall Problem with Ron Clarke”, this video starts with “Hello and welcome to the Monty Hall problem, with me Ron Clarke.”
2. Write a paper that includes:
   1. What you thought the answer was; (3 points)
   2. Information from the video what the answer really is (3 points)
   3. How was probability used in arriving at the answer? What probability ideas does this demonstrate and use? Explain and give examples. You may use other sources as well but make sure to cite them. (15 points)
   4. Are you surprised by the answer to the question “stay or switch”? Does it make sense? (3 points)
   5. 2 pages long, using size 12 font and double spaced. (3 points)
   6. a cover page and a references page (at least the YouTube video should be included)(3 points).

Suppose that a class contains 15 boys and 30 girls, and that 10 students are to be selected at random for a special assignment. Find the probability that exactly 3 boys will be selected. 

Instructions:

minimum of 300 words NO PLAGIARISM and your solution must reflect your understanding of the question posed.  In addition to the computations you employed to arrive at your response, your answer must contain comments regarding the rationale for the approach you utilized.  Simply listing an answer is of no real value in promoting a discussion.

probability

1. A normal population had a mean of 60 and a standard deviation of 12.
A random sample of 36 units is drawn from the population. Find:
a) The standard error of the mean.
b) The probability that the sample mean is less than 62.
c) The probability that the sample mean is between 58 and 61.
d) The probabilty that the samp[le mean is between 56 and 59.

2. A random sample of 25 apples were take from a large apple tree and were weighted.
The mean weight of an apple in the sample was found to be 8 oz.
The weights of apples in the tree were known to be normally distributed with a standard
deviation of 1.5 oz. Find:
a) The 90% confidence interval for the population mean.
b) The 95% confidence interval for the population mean.

3. A random sample of 16 workers in large factory had an average hourly rate of $10.
The nsample standard deviation was $2.
The hourly rates of workers in the factory is assumed to be normally distributed.
Using Student t Distribution find:
a) The 90% confidence interval for the population mean.
b) The 95% confidence interval for the population mean.

4. In a random sample of 100 customers in a store 60 customers paid their
bills with credit cards. Find:
a) A point estimate of the proportion of all customers at the store who pay with
credit cards.