00:01
The weights of full -grown old english sheepdogs are normally distributed so we could draw the bell -shaped normal curve.
00:11
The mean will place at the center is 69 pounds and the standard deviation is 3 .9 pounds.
00:22
And we want to determine the probability that a new puppy of this breed will eventually when, more than 75 pounds.
00:35
So 75 pounds would be above the mean and weighing more than 75 would be represented by the area in the right tail.
00:47
So in order to calculate this, we would have to find the z score associated with 75 pounds.
00:55
And to find the z score, we're going to apply the formula x minus mu over sigma.
01:00
So we'll put 75.
01:02
Minus 69 divided by a standard deviation of 3 .9, which gets you the z score of 1 .5384 -61158.
01:18
So that means the probability that x is greater than 75 is no different than the probability that z is greater than approximately 1 .54.
01:32
So if we go to the back of your textbook, there is a standard normal table.
01:38
And down the left side, we are going to look for the ones and tenths place.
01:46
And across the top, we're going to look for the nearest hundredths place.
01:50
So this three, because of the eight, would be rounded to a 1 .54.
01:58
So across the top, we'd be looking for the 0 .04.
02:03
And in doing so, you're going to find an area, and that area is going to be 0 .93822.
02:11
Now, your table may not go out to five decimal places.
02:14
Yours might only go out to three or four, and it'll still work the same way.
02:20
And that area represents the area in the left tail.
02:24
So that means from that z score back into the left tail is an area of 0 .93822.
02:33
So if i want to find the area in the right tail, i would have to think about the fact that the left plus the right always adds up to one.
02:41
So it's in the right tail will be one minus the area in the left tail.
02:49
So therefore, when i subtract that out, i will get a probability of 0 .06178.
02:59
Now with part b, we want to know is this considered usually? or unusual.
03:07
And we would say an old english sheepdog that weighs more than 75 pounds is not unusual because the probability of that happening is greater than 0 .05...