Stats & probability Read and follow the directions below and answer all question
ID: 3252681 • Letter: S
Question
Stats & probability
Read and follow the directions below and answer all questions! Do not do this problem unless you are going to answer them all! I will rate!
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For the following questions please include the results of your data collection and then enter your answer. For example, if you are asked to roll a single die 10 times you might write:
4 2 1 1 3 6 5 2 4 3
P(3) = 2/10 = 0.20
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1.) A bone study that measures a biomarker, TRAP, yields a mean of 13.2 units/liter. Assuming the standard deviation is 6.5 units/liter, what sample size would be required at a 95% confidence to get a margin of error of 1.5 units/liter?
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2.) Draw 3 cards without replacement (in other words, draw the top 3 cards from a shuffled deck), repeat this 10 times (for fairness you should reshuffle the cards between each set of 3 cards). Determine the following probabilities from your results
A.) P(one of the cards is a spade)
B.) P(All 3 cards are a Face card AND club)
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3.) Calculate the theoretical probability of getting the following and compare them to your randomly generated results above.
A.) P(one of the cards is a spade)
B.) P(All 3 cards are a Face card AND club)
Explanation / Answer
1)
mean = 13.2
standard deviation = 6.5
margin of error = 1.5
let sample size be n
standard error = 6.5/n
margin of error for 95% confidence interval = 1.96*standard error = 1.96*(6.5/n)
1.96*(6.5/n) = 1.5 => n = 1.96*6.5/1.5
n = 8.4933
n = 8.49332 = 72.136 i.e 73 as 73 is next integer
sample size would be required at a 95% confidence to get a margin of error of 1.5 units/liter is 73