According to National Vital Statistics, the average length...

According to National Vital Statistics, the average length of a newborn baby is $19.5$ inches with a standard deviation of $0.9$ inch. The distribution of lengths is approximately Normal. Use a table or technology for each question. Include an appropriately labeled and shaded Normal curve for each part. There should be three separate curves. an What is the probability that a baby will have a length of $20.4$ inches or more? b. What is the probability that a baby will have a length of $21.4$ inches or more? c. What is the probability that a baby will be between 18 and 21 inches in length?

Transcript

00:01 All right.

00:01 In your question, you're given a mean of 19 .5 inches and a standard deviation of 0 .9 inches for newborn baby length at birth.

00:11 And i'm going to state that x, i'm going to let x equal baby length.

00:15 And that helps me write out the questions that you're being asked.

00:19 So in part a, you're asked for the probability that x or the baby's length is greater than or equal to 20 .4.

00:26 You're allowed to use technology or a table to help you solve this.

00:29 Okay, so, and you're also to include properly labeled and shaded sketches for each question.

00:38 So this region up here is going to be for part a.

00:41 This will be for part b.

00:42 This will be part c.

00:44 The question stated a normal distribution.

00:47 So you should have a normal bell -shaped curve.

00:50 And for each of those distributions, we would expect 19 .5 to be at the center or the mean.

00:56 In question a, i should add the, a mark roughly in this region of 20 .4 to represent what we're working on for a probability.

01:09 We would then draw in a vertical boundary line, and we're interested in the probability of being greater than that, so we would shade to the right.

01:19 So we want to shade it in this region.

01:25 Okay, so let's go ahead and finish the drawings for each problem, and then we'll calculate the probabilities.

01:34 For part b, we want to find the probability that x is greater than are equal to 21 .4.

01:40 So that should be reflected in your drawing to be a little bit further out than the last one was.

01:50 And again, shade to the right.

01:56 And finally, the last question, we were going from 18 to 21.

01:59 So that would be rough in this region to this region.

02:10 And then i would shade between those two regions for our probability.

02:25 Okay, so moving on to actually calculating these.

02:28 Since it said we could use technology, i'm going to use a program called normal cdf.

02:34 You could find that on the internet just by typing it into a search engine, or you may have a scientific calculator that has that.

02:42 I'm using a ti -84 calculator.

02:46 And normal cdf is found under the second distribution key.

02:55 And the first thing it's going to ask for is the lower boundary...

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