00:01
In this problem, let x will be the weight of dog and we know that variable x has the normal distribution.
00:12
Population mean mu is 45 and population standard deviation sigma is 3.
00:23
Task a.
00:29
If one dog is selected at random, find the probability that his height is within one pound of the mean weight of 45.
00:39
This can be written as we should find the probability that x will be between 44 and 46.
00:51
This equals probability that x is less than 46 minus probability that x is less than 44.
01:04
Let's find that score values.
01:07
Probability that is less than 46 minus 45 divided by 3 minus probability that z is less than 44 minus 45 divided by 3.
01:27
And we obtain probability that z is less than 0 .333 minus probability that z is less than 0 .333 minus probability that z is less than minus 0 .333.
01:46
And by using that score table, we can find the corresponding probabilities 0 .6304 minus 0 .3696.
02:04
And we obtain 0 .2608.
02:09
So this is the answer for the part a.
02:12
The next part b.
02:18
If 40 dogs are randomly selected, find the probability that the sample mean weight is within one pound of the mean weight of 45...