Use normal table to solve this problem weekly demand at a...

Use Normal Table to solve this problem Weekly demand at a grocery store for a brand of breakfast cereal is normally distributed with a mean of 800 boxes and a standard deviation of 75 boxes. What is the probability that weekly demand is less than 959 boxes? What is the probability that weekly demand is more than 1,004 boxes? What is the probability that weekly demand is between 650 boxes and 950 boxes? If the store orders cereal from a distributor weekly. How many boxes should the store order for a week less than 97.5 percent needed of this brand of cereal during the week?

Transcript

00:01 So in this problem, we're told that the weekly demand for a brand of breakfast cereal in a grocery store is normally distributed with a mean of 800 and with a standard deviation of 75.

00:14 We then have four different questions here to answer.

00:18 So we'll start off with the first one, which asks, what is the probability that weekly demand is less than 959 boxes? so here we're finding the probability that x is less than 959.

00:31 The first thing we need to do is to find a z score for 959 using this red equation i have on the screen.

00:38 So using the equation, z is equal to x, which is 959, minus the mean, which is 800, then divided by standard deviation, which is 75.

00:49 This gives us a z score of 2 .12.

00:53 So now let's turn to our z table on the left of the screen and find 2 .12.

00:58 We go down on the left to 2 .1, over on the right to 0 .02.

01:02 And we get .9830.

01:10 So our z table always gives us what is less than what we're trying to find.

01:15 So this probability here is the probability of x being less than 959, and that's what we want, remember.

01:21 So this is our final answer.

01:23 It's about a 98 .3 % chance that the weekly demand will be less than 959 boxes.

01:33 Now for part b, part b asks us to find the probability that weekly demand, is more than 1 ,004 boxes.

01:40 So now we're finding the probability that x is greater than 1 ,004.

01:45 So now let's find a z score for 1 ,004 using the same equation.

01:50 So z is equal to x, which is now 1 ,00, minus the mean, divided by the standard deviation, and when you calculate that, you get 2 .72 as the z score.

02:02 If we find that in our table, 2 .72, we get point 7 .2.

02:11 Now remember this is the probability of x being less than 1 ,004.

02:16 So to find the probability of x being greater than 1 ,004, we have to subtract this from 1.

02:21 So we'll take 1 minus 0 .9967 and we get 0 .0033.

02:28 So there's just a 0 .33 % chance of weekly demand being greater than 1 ,004 boxes.

02:36 Part c, we're asked to find the probability weekly demand is between 650 and 950 boxes.

02:43 So we're finding the probability that x is greater than 650 and less than 950.

02:51 So now what we need to do is find a z score for both at 950 and 650.

02:57 So we'll start off with 950...

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