Suppose that the weight of navel oranges is normally...

Suppose that the weight of navel oranges is normally distributed with mean µ = 8 ounces and standard deviation σ = 1.5 ounces. We can write X ~ N(8, 1.5). Answer the following questions: (a) What proportion of oranges weighs more than 10.2 ounces? (b) If you randomly select a navel orange, what is the probability that it weighs less than 6.9 ounces? (c) What proportion of oranges weighs between 5.5 and 7 ounces? (d) Find the 80th percentile of this distribution of X. (e) Find the interquartile range of this distribution of X.

Transcript

00:01 Alright, so we have this normal distribution with a mean of 8 and a standard deviation of 1 .5.

00:07 So we are first, i'll just go ahead and draw a little normal distribution here to do my drawings on.

00:16 First we're asked what proportion of oranges weigh more than 10 .2 ounces.

00:22 So if we have our z formula, z equals x minus mu over sigma, then for this a, our x is going to be that 10 .2.

00:30 So this will be 10 .2 minus 8 over 1 .5.

00:37 And when i have that z, it comes out to 1 .47 approximately.

00:44 And then when i look up that on the table, and i make sure to look at the right tail, not the left tail, that comes out to an area of 0 .0712.

00:55 Okay, so that is the proportion of oranges that weigh more than 10 .2.

01:01 Ounces is 0 .0712.

01:05 Okay.

01:06 For b, what's the probability that an orange weighs less than 6 .9.

01:11 So once again, i'm going to do my 6 .9 minus 8 over 1 .5.

01:17 Get my z statistic of negative 0 .73.

01:23 This time, when i'm looking at my distribution, i need to make sure i'm looking at the left tail because i want all the values that are less than 6 .9.

01:34 And when i look up that negative .73 on the table, i end up getting .2317 for that area there.

01:43 Okay? for c, i want the proportion that are between 5 .5 and 7.

01:50 So i'm actually going to do two z statistics here, one for 5 .5 and one for seven.

02:02 Each of those z statistics comes out to, for this one.

02:06 Negative 1 .67 and when i look up negative 1 .67 on my table which it's about right there right i get that this area here is 0 .0478 and then for the other z that comes out to negative 0 .67 and when i look up that value okay this entire blue area right here okay comes out to negative 0 .67 and when i look up that value okay this entire blue area right here okay comes out to to 0 .2525.

02:44 So if i'm looking for this red area right here, right, the value between those two, i need to subtract my blue area and my black area...

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