00:01
There is a normal distribution for the question and the given mean value, the mean, which is new, that is 60 ,000, and the standard deviation, that is at 10 ,000 miles.
00:15
So in part a, let's say x is the random variable here, and normally distributed, that is 60 ,000 and 10 ,000.
00:25
So in part a, what we have to find, what's the probability that random selected fire will have a life, at most 80 ,000.
00:33
So the probability of x is less than or equal to 80 ,000.
00:41
And so what we have to do, let me just graph the situation here and we can easily see where we have to find.
00:49
So the mean value here is 16 ,000 and the 80 ,000 is over here.
00:55
So we have to find the area of this region.
00:59
So for this area, we have to use the normal cdf.
01:04
And the lower boundary here is negative infinity.
01:07
So we have to put negative 1e99.
01:09
That means negative infinity.
01:11
The upper boundary is 80 ,000.
01:15
And the standard deviation, i mean, the mean value here is 60 ,000.
01:22
And the standard division is 10 ,000.
01:25
So let's put all these numbers to the calculator and get the result.
01:29
Second distribution, normal cdf.
01:31
Lower boundary is negative 1 and this is e99 and comma the upper boundary is 80 ,000 comma mean value is 60 ,000 and the standard division is 10 ,000 and get the result which is equal to that is 0.
01:51
0 .772 that is the answer for part a.
01:57
What about for part b? what is the problem? what is the and the most selected tire will have a life of at least 60 ,000.
02:05
So we have to find the p is greater than or equal to 60 ,000.
02:10
So that means if i draw again the bell shape here, this is the mean, that is 60 ,000...