00:01
Firstly, let's summarize this problem, that x will be the reaction time, and we know that variable x follows the normal distribution, with population mean mu equal 25, and population standard deviation sigma is 3.
00:21
Task a, we should find the probability that x will be between 14 and 30.
00:33
This equal probability that x is less than 30 minus probability that x is less than 14.
00:48
Let's find that score values.
00:51
Probability that z is less than 30 minus population mean 25 divided by standard deviation 3 minus probability.
01:05
That z is less than 14 minus 25 divided by 3.
01:15
And we obtain probability that that is less than 1 .66 minus probability that z is less than minus 3 .66.
01:31
And by using that score table, we can find the corresponding values of probability 0 .9515 minus 0 .001.
01:50
And we obtain 0 .9514.
01:56
So this is the answer for the part a.
02:01
The next part b, we should find the probability that x will be greater than 14.
02:12
This will be 1 .1.
02:12
This will be 1.
02:14
Minus probability that x is less than 14.
02:21
Let's find that score value 1 minus probability that is less than 14 minus 25 divided by 3.
02:34
And we obtain 1 minus probability that z is less than minus 3 .66.
02:44
And by using that score table, we can find the corresponding value of probability 1 minus 0 .0001 and this will be 0 .999.
03:07
So this is the answer for the part b.
03:11
The next part c, we should find the value of the reaction time that corresponds to the top 2.
03:22
Percent of the data.
03:25
So this can be written as probability that x is greater than unknown value x equal 0 .02 or 2 percent.
03:38
Next probability x is less than unknown value x equal 1 minus 0 .02 and probability that z is less than unknown value z will be 0 .98.
03:57
And by using that score table, we can find the corresponding value of that score, and we can write the probability that is less than 2 .05 equal 0 .0.
04:16
9 .8.
04:19
Now let's remind the formula for the z score, x minus mu divided by sigma...