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Given mean = 167cm, standard deviation is 3cm,

a) When four are randomly selected, all of their heights will be greater than 170?

b) When four are randomly selected, two will have heights smaller than the mean, two will have heights greater than the mean?

For a) it is just [P(Z > 1)]^4 = 0.00063

For b) it is (0.5)^2 + (0.5)^2

Is my methodology correct?

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For (b), they are chain events, and should be multiplied. If there were two people, your calculation would give 0.5+0.5=1. Also, we need to consider the possible number of combinations, i.e. ${4 \choose 2} p^2(1-p)^2$, where $p=0.5$.

For the first one, probability seems correct but I just want to make sure that you need to read $P(Z>1)$ from the table.

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  • $\begingroup$ Ah, completely forgot about the number of combinations. So the answer to b) would be 6*0.25*0.25. $\endgroup$
    – Crystal McMillian
    Jan 18, 2019 at 5:40
  • $\begingroup$ Yes, that’d be correct. $\endgroup$
    – gunes
    Jan 18, 2019 at 6:17

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