0
$\begingroup$

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?

$\endgroup$

1 Answer 1

0
$\begingroup$

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.

$\endgroup$
2
  • $\begingroup$ Ah, completely forgot about the number of combinations. So the answer to b) would be 6*0.25*0.25. $\endgroup$ Jan 18, 2019 at 5:40
  • $\begingroup$ Yes, that’d be correct. $\endgroup$
    – gunes
    Jan 18, 2019 at 6:17

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.