Some sources report that the weights of full-term newborn...

Some sources report that the weights of full-term newborn babies in a certain town have a mean of 9 pounds and a standard deviation of 1.2 pounds and are normally distributed. a. What is the probability that one newborn baby will have a weight within 1.2 pounds of the mean—that is, between 7.8 and 10.2 pounds, or within one standard deviation of the mean? b. What is the probability that the average of four babies' weights will be within 1.2 pounds of the mean; will be between 7.8 and 10.2 pounds? c. Explain the difference between (a) and (b).

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00:01 There is given a normal distribution.

00:02 The mean and the standard deviation was given here.

00:05 So the mean denoted by mo that was given as nine pounds in the standard deviation.

00:11 So the standard deviation, which is denoted by sigma, that was given as 1 .2 pounds.

00:17 And this is a normal distribution.

00:19 I can define the random variable x, which is normally distributed.

00:21 This is 9 and 1 .2.

00:23 And let's take a look at the first one here.

00:26 And there's a one newborn baby, which is between.

00:30 7 .8 and 10 .2, which is within one standard one point one standard division away from the mean or 1 .2 pounds of the mean because the standard division was 1 .2.

00:42 Let me just find the probability here, which is the axis between.

00:45 If i add 1 .2 to the mean value, that was 10 .2.

00:50 If i subtract them, we have 7 .8.

00:54 In order to get this probability, i'm going to use the graphing display calculator application, which is normal cdf.

01:00 So the lower bound.

01:01 Is 7 .8, the upper boundary is 10 .2, the mean is 9, and the standard division is 1 .2.

01:06 Let's get the answer.

01:08 Press second variance, the second option here, the lower boundary is 7 .8, the upper boundary is 10 .2, and the mean is 9 and the standard division, which is 1 .2...

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