The weights of newborn babies vary according to a normal...

The weights of newborn babies vary according to a normal distribution with a mean of 7.5 pounds and a standard deviation of 1.25 pounds. A newborn baby with a weight less than 5.0 pounds is considered to have a low birth weight. A) If an individual is selected, find the probability that the individual's birth weight is less than 5.0 pounds. B) If a sample of 2 babies is selected, find the probability that their average birth weight is less than 5.0 pounds. C) If a sample of 4 babies is selected, find the probability that their average birth weight is less than 5.0 pounds. D) What is the maximum weight of the bottom 1% of newborn babies? A diagram will help.

Transcript

00:01 Hi, i'm david and i'm here to have you answer your question.

00:03 Now let me bring up your question here.

00:07 In this question we will discuss about the normal distribution.

00:11 Here, let me remind you that if we have the x, it followed by the normal with the mean and the standard deviation.

00:18 Then if we turn the x minus the mean of a standard division, it will follow by the standard normal.

00:24 Also if we discuss about the sample mean x bar minus the mean of a standard division, but we need to divide by square of n as well to obtain the standard normal.

00:35 Here we are given that the x it will follow by x will be the weight of the new baby and it will follow by the normal which means equal to the 7 .5 standard division equal to the 1 .25 and now the question i asked us to find the probability that the individual birth weight is less than 5.

01:08 So x will be smaller than 5.

01:11 Now, in that you find this probability, we need to turn the x into the z by using this formula.

01:18 So to do that, we have to write the 5 minus the mean of a standard deviation.

01:27 And then we obtain the z will be smaller than 5 minus the 7 .5 divided.

01:35 By 1 .25 equals minus 2.

01:39 Now this one we can bring up the z table and we show you have to use the z table here and let me put the table down here for you.

01:53 Now from the table we will have the z score equal to minus 2.

01:58 So we have it will be the minus 2 here and the corresponding probability equal to the 0 .0228.

02:08 And that's going to be the answer for the part a.

02:12 Now for the part b, 1 -25, if the symbol of 2 by b, so now n equal to 2, for the proper between the average weight, it means that i want to find proper by the x bar.

02:25 It will be less than 5.

02:28 For the x -bar, we need to use the formula for the x -bar here.

02:34 So we will obtain the z smaller than 5 minus mean.

02:38 Our standard deviation but we have to divide by the square root of n which is 2...

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