Suppose the amounts of sugar intake for adults follow a...

Suppose the amounts of sugar intake for adults follow a normal distribution with an average of 77 grams per day and a standard deviation of 7 grams per day. Draw appropriate sketches in each case and answer the following questions: a) [3] Find the probability that a randomly chosen adult eats between 75 grams and 80 grams of sugar per day. b) [3] Suppose adults whose sugar intakes are in the top 2% among the population need more medical investigations. What is the minimum amount of the sugar intake of the top 2%? (cut-off point) c) [6] A sample of 100 adult was selected at random. What is the probability that the average sugar intake of the sampled adult is less than 78 grams per day? (explain all the steps; the distribution and its parameters) d) [2] Suppose we did not know that the amounts of sugar intake for adults follow a normal distribution, would you still be able to find the distribution of the statistic of interest in part c?

Transcript

00:01 So here we're talking about the normal distribution, right? we have this idea that sugar, which i'm just going to call x, is distributed normally with a mean of 77 grams per day and a standard deviation of 7 grams per day.

00:14 So we need to calculate some probabilities, right? so for a, though i meant to do that in blue, for a, we're thinking about the probability that x is between 75 and 80.

00:28 Well, if i was going to graph that, right, we need to think about, say, the normal distribution, it shouldn't even draw that vertical line, right? the normal distribution, which looks something like this, here's the mean at 77.

00:43 We want to target between 75 and 80, right? so this is the probability that we're interested in isolating.

00:52 Now, there's many, many, many ways to do this.

00:55 I'm going to try to go through a couple ways.

00:58 So the first way i'm going to do it is via excel.

01:01 Right? if you're interested in doing this excel, it's norm .dust.

01:05 That's the function that calculates normal probabilities.

01:08 80, 77, 7, and true.

01:12 And that function says, give me all the probability below 80, right? this is the probability that x is less than 80.

01:20 Give me the probability less than 80 if mean is equal to 77 and sigma is equal.

01:28 With a seven.

01:29 That's what that function is saying, right? the distribution below 80, if the distribution is centered around 77 with a 7 standard deviation.

01:36 So this gives me all the way back.

01:38 I need to subtract off what's below 75 minus norm .dd.

01:45 75, 77, 7 and true, right? punch this into your spreadsheet.

01:54 Again, just one of many, many ways to do this, but it's impossible to do these questions.

01:58 By hand the normal distribution is just too complicated and that should give us a relatively small number right i know it's a relatively small number because it's just not that much of the area right we're not even capturing one standard deviation so it's simply not that much of the distribution right so b i b, we want to think about the top 2%...

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