Question

Please, answer the questions 5,6,7,8,9,10. Add explanations if possible.

Use the following simulation to answer the questions. Assume you are flipping an unfair coin 20 times and calculating the proportion of times the 20 flips turn up heads. You repeat this 100 times and the simulation output is as follows. The probability of this unfair coin to come up heads is 0.40 Probability of success (TT): 0.4 Summary Stats Sample size (n): 20 Mean .0400 Number of samples: 100 SD 0.108 Animate Draw Samples Total- 100 2 Number of successes Proportion of successes As extreme as Count 0.10 020 030 0.40 0.50 000 0.70 Proportion of successes Question 5 What is the probability that at most 6 of 20 flips are heads? Question 6 Should we consider this event "unlikely"? O Yes O No Question 7 ty that 4 or fewer flips are heads out of 20 flips? Round to 3 decimal places. Question 8 Should we consider this event "unlikely" o Yes O No Question 9 What is the probability that at least 11 of 20 heads are flipped Question 10 Should we consider this event "unlikely"? O No Yes

Answer 1

Question 5:

Sol:

  Probability that at most 6 of 20 are heads :

Probability of heads = 6/ 20 = 0.3

No of instances for P(X <= 0.3) = 21

Probability that at most 6 of 20 are heads = 21/100 = 0.21

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