Yesterday, 1/4 of 80 =20 gave their speeches, so there are 80-20=60 students left. Today, 2/5 of 60=24 students gave their speeches, so there are 60-24=36 students who still haven't give their speeches another way to think of it is 80*(1- 1/4)*(1- 2/5)=80*(3/4)*(3/5)=36
And we can find this probability with the normal standard distirbution or excel and we got:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the lenghts of a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability with the normal standard distirbution or excel and we got:
4.15, 6.3, 8.45, 10.6, 12.75 You just subtract 4.15 from 6.3 and you get a difference of 2.15. Then you add it to 8.45 giving you the answer of 10.6 and then you add 2.15 to that getting 12.75.