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# Probability and Statsitcs (SMOG and FOG tests)

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I am a mature student (age 60) currently working for a training company. I have been asked to complete a training project which involves these questions and have already done some of the work; however, I need to confirm my answers for these last few questions.

I have attached the questions along with the SMOG and FOG data sheets

Questions:

Probability

1. A chef in a restaurant takes three rice dishes at random, without replacement, from a freezer. The freezer contains 4 fried rice dishes and 3 boiled rice dishes.
a) Show all the possible outcomes and their probabilities using a tree diagram.
b) Find the probability that exactly two boiled rice dishes are taken.
c) Find the probability that the first dish taken is the same type as the third.
d) What underpinning skills are used to complete these activities?

Statistics

2. I have carried out a SMOG and FOG test on a number of pieces of text from mathematics text -books. The results are attached as a spreadsheet.
I need the data appropriately grouped and an estimate of the mean for each of the groups.
a) Produce a cumulative frequency curve for each of the results and identify the median and upper quartiles.
b) Use a box and whisker diagram to determine the interquartile range.
c) Compare the results and draw conclusions about the accessibility of the various texts.
d) Produce a scatter diagram to determine whether there is any correlation between the results from the SMOG and FOG tests using a spreadsheet or other graph plotting software to complete the task.

3. Many tests taken by students such as IQ tests are designed to be normally distributed with a mean of 100, and standard deviation of 15.

Show whether the following statements are true

a) 68% of all people should gain a test score between 85 and 115
b) Only 6% of people have a test score of less than 70
c) There are very few people who will get a test score of more than 145
d) To pass the test, students would have to gain a test score of above 85. How many of the students are likely to pass?

4. Summarise the factors to be considered in planning a data collection activity e.g. types of data, sampling methods, bias etc.
a) Detail how each of these factors impacts on data collection
b) Suggest one way the data in the attached table could be presented and give reasons for the answer.

1. If we were to test a hypothesis such as " people with small wrist circumferences will also have small waist sizes" using statistical methods, how would we decide if the hypotheses was true?

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