Mathematical Problem “Statistical Thinking Worksheet “

Q.1 There are 23 people at a party. Explain what the probability is that any two of them share the same birthday.

Answer and explanation

In a year, there are 365 days, when it’s one person, the probability is 1/365, but if it’s two people, the chance increase to 2/365.

1/365*2=2/365=0.00548.

But this is only when there are two people, yet we are told it is 2 out of 23, so we divide the answer above by 23

0.00548/23 to obtain the final answer which is 0.000238 or (2.38*10power -4)

Q.2 A cold and flu study is looking at how two different medications work on sore throats and fever.  Results are as follows:

 

  • Sore throat – Medication A: Success rate – 90% (101 out of 112 trials were successful)
  • Sore throat – Medication B: Success rate – 83%  (252 out of 305 trials were successful)

 

  • Fever – Medication A: Success rate – 71%  (205 out of 288 trials were successful)
  • Fever – Medication B:  Success rate – 68%  (65 out of 95 trials were successful)

Analyze the data and explain which one would be the better medication for both a sore throat and fever.

The answer is Medication A. this is because when you look at the percentage of success rate, the medication has a higher success rate in both a sore throat and fever.

In a sore throat the success rate was 90% in comparison to drug B, which was 83% while in Fever, the success rate was 71% in comparison to drug B, which was 68%. Even though the total number of people tried varies, the success rate in percentage is not dependent on the number, but it is a standardizing factor. If the total number of people tried on medication be was increased, it only means that there would have been a high number of individuals affected by the drug on trial. I.e. failure of it performing the expected function.

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Q.3 The United States employed a statistician to examine damaged planes returning from bombing missions over Germany in World War II.  He found that the number of returned planes that had damage to the fuselage was far greater than those that had damage to the engines.  His recommendation was to enhance the reinforcement of the engines rather than the fuselages.  If damage to the fuselage was far more common, explain why he made this recommendation.

This is because the probabilities of a plane not to function when hit on the engine is high in comparison to the possibility of it not working when hit on the fuselages. This can be explained by the fact that many planes had been damaged to the fuselage, yet they had returned.

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