Project #22960 - Statistics Quiz

I need someone to do this quiz very quickly!

For the problems that require a written response, please use proper English and complete sentences.  Your definitions and explanations should be explicit and meaningful from a statistical viewpoint.  Where appropriate, fill in the space with the required missing term or value.  For the computational problems, show all essential work, but please make use of your calculator's statistical keys.  There are 15 problems each worth seven points.  Express your answers, as appropriate, in reduced fractional form or rounded to the nearest hundredth or thousandth or to the nearest tenth of a percent.  Do well!

1.    A Chinese restaurant offers only a \$20 per person buffet at lunch, which includes one fortune cookie at the end of your meal.  Seventy-five percent of these fortune cookies contain the usual sort of fortunes (which is a slip of paper with some ominous message written on it), 20% contain immediate discount coupons for \$2 off the lunch buffet price, and 5% contain a message that your buffet lunch today is free of charge.  Find a diner's expectation for the actual amount paid for his/her buffet lunch at this restaurant ORconstruct a probability distribution for the actual amount paid for a buffet lunch at this restaurant.

2.    For Valentine's Day you received a box of homemade filled chocolates.  All the chocolates look identical, however the fillings vary.  Due to the jostling of the box, the chocolates are randomly arranged in the box.  Seven of them are filled with peanut butter, twelve are filled with cherries, and sixteen are filled with marshmallow cream. If three of these chocolates are randomly selected, one at a time and eaten as selected, what is the probability that all three are filled with cherries?

3.    A florist has roses in seven different colors, two kinds of vases, and five different style gift cards.

a)  How many ways can a client select one color of rose, one vase, and one gift card?

b)  How many ways can a client select three different colored roses and arrange them in a row in a flower arrangement?

4.    A random sample of 36 farms west of the Mississippi indicated a mean size of 428 acres.  Nationwide, the average farm size is 444 acres with a standard deviation of 52 acres.

a)  Calculate the z-score for the mean size of a farm west of the Mississippi.

b)  If we took all samples of size 36 and calculated the sample means, could we justifiably claim that the distribution of all those sample means is approximately normally distributed?  Yes or no and why or why not?

5.    Using the standard normal distribution, find:  P(-1.62 < z < 2.04)

For Problems 6 and 7, refer to the following information.

A political scientist randomly selected 100 eligible voters and determined the number of times they had voted in the last two general elections:

Number of

Times Voted       Probability

X               P(X)

0               0.1

1               0.05

2               0.85

6.    What is the mean number of times voted?

7.    What is the standard deviation of this distribution?

For Problems 8 and 9, refer to the following information.

To qualify for security officers' training, recruits are tested for stress tolerance.  The scores are normally distributed, with a mean of 62 and a standard deviation of 9.

8.    Find the probability that a randomly selected recruit scores below 55.

9.    If only those who score in the top 14% are selected for security officer's training, what is the cut-off score to qualify?

For Problems 10-12, refer to the following information.

Approximately 30% of American university graduates graduate without any debt.  For a random sample of 18 recent American university graduates, answer the following:

10.  Find the probability that 5 or 6 of them graduated without any debt.

11.  Find each of the following:

a)  the expected number who graduated debt free in this group of 18 graduates.  That is, find the mean of this distribution.

b)  The standard deviation of this distribution.

12.  Could this binomial distribution be reasonably approximated by a normal distribution?  Yes or no and why or why not?  Support your answer with numerical evidence actually stating the numerical value(s).

For Problems 13-15, refer to the following information.

The five Olympic rings represent the five inhabited continents: Africa, Americas, Asia, Europe, and Oceania.  The medal distribution of the 2010 Winter Olympics for those continents is shown in the table below.

 Medals Continents Gold Silver Bronze Totals Africa 0 0 0 0 Americas 23 22 18 63 Asia 14 17 15 46 Europe 47 47 52 146 Oceania 2 1 0 3 Totals 86 87 85 258

If one of these medals is randomly selected,

13.  what is the probability it will be a bronze medal or it was awarded to the Americas?

14.  what is the probability that it was awarded to Europe given that the medal selected is gold?

15.  what is the probability that the medal selected was not awarded to Asia?

 Subject Mathematics Due By (Pacific Time) 02/16/2014 02:15 pm
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