For each statement determine the range of birth weights that...

For each statement, determine the range of birth weight(s) that encompass the stated percentages of weights. Include each bullet within each answer. Embed a picture of the probability density curve that represents the problem include all the important labels, shading, and proper notation. Show your work, include any Excel formulas used, and restate the answer in context of the problem. Round the weights to one decimal place if needed. i. The middle 70% for 32 to 35 weeks.

Transcript

00:01 The distributions of birth weights for three gestation periods are shown.

00:06 Match each curve with a gestation period and explain your reasoning.

00:12 Now we're missing the little table, and the little table has gestation periods, and means and standard deviations.

00:22 So matching up the, probably the easiest thing to do is match up the mu.

00:28 So for a, we're looking for a mu that's between 7 and 8, there's only one gestational period that has that, and that's 39 to 40 weeks.

00:38 For b, we're looking for a mu that is between 4 and 5, and 32 to 33 weeks has a mu that matches up to that.

00:49 And then for c, 34 to 36 weeks matches up with a mu that's between 5 and 6, closer to 6 than 5.

00:58 So that would be the good matchup for that one.

01:03 For number two, what percent of babies born within each gestation period have a low birth weight under 5 .5 pounds? so again, you're going to need to look at your table for each of these.

01:16 So for a, we're finding the probability that z is less than 5 .5 minus.

01:24 So for 28 to 31 weeks, that has a mu of 3 .2 and a standard deviation of 1 .02.

01:33 So the probability that z is less than 2 .2.

01:37 Which has a probability of 0 .9878.

01:42 For b, a gestation of 32 to 33 weeks has a mu of 4 .31, divided by a standard deviation of 0 .97.

01:56 So i'm pulling that right off the table.

01:59 That gives me a z value of 1 .23, which has a probability of 0 .8907.

02:08 So you're going to follow that same process for part c and d.

02:13 Using the mu and standard deviation off of your table that's in your book for the gestation periods.

02:20 So for three, now we're going to describe the weights of the top 10 % of babies.

02:26 So before i start with that, i want to find the 90th percentile in my standard normal table, and the 90th percentile is 1 .28.

02:36 So for a, under 28 weeks, i'm going to take the mean from the table, which is 1 .60 plus the standard deviation times that z value.

02:52 So 1 .28.

02:55 There you go.

02:57 And that is going to give me 2 .57...

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