Question

3. A coin is tossed 140 times. The probability of getting tails is p = 0.500. Would a result of 55heads out of the 140 trials be considered usual or unusual? Why?Unusual, because the result is less than the maximum usual value.O Usual, because the result is between the minimum and maximum usual values.Unusual, because the result is less than the minimum usual value.Unusual, because the result is more than the maximum usual value

Answer 1

In order to calculate the minimum and maximum usual values, first let's calculate the mean and standard deviation of this distribution:

`\begin{gathered} \mu=n\cdot p=140\cdot0.5=70\\ \\ \sigma=√(np(1-p))=√(140\cdot0.5\cdot0.5)=5.92 \end{gathered}`

Now, calculating the minimum and maximum usual values, we have:

`\begin{gathered} minimum=\mu-2\sigma=70-11.84=58.16\\ \\ maximum=\mu+2\sigma=70+11.84=81.84 \end{gathered}`

Since the given result is 55, it is an unusual reslt, because it is less tahan the minimum usual value.

Correct option: third one.