Ssume that the duration of human pregnancies can be...

ssume that the duration of human pregnancies can be described by a Normal model with mean 264264 days and standard deviation 1515 days. a) What percentage of pregnancies should last between 267267 and 279279 days? b) At least how many days should the longest 3030% of all pregnancies last? c) Suppose a certain obstetrician is currently providing prenatal care to 5555 pregnant patients. Let y overbary represent the mean length of their pregnancies. According to the Central Limit Theorem, what is the distribution of this sample mean, y overbary? Specify the model, mean, and standard deviation.

Transcript

00:01 There is given a normal distribution for this question.

00:04 The mean value was given.

00:05 So the mean, which is denoted by moot, this is 266.

00:09 And the standard deviation, which is denoted by sigma, that was given as 17 days.

00:16 And i can define the random variable x, which is normally distributed to 66 and 17.

00:22 So what we're going to find in part a, we need to find the percentage of the pregnancies should loss between.

00:29 So we need to get the probability of random variable x, which is between 268 and 277.

00:36 In order to get this probability, i'm going to use the normal cdf function for the graphing display calculator.

00:41 The lower boundary is 268, the upper boundary is 277, and the mean value is 266 and the standard division, which is 17.

00:51 Let's get the answer.

00:53 Press second.

00:54 Press second variance, the second option here.

00:56 The lower boundary, 268, and the upper boundary is 277.

01:01 And the mean is to 66 and the standard division which is 17 so we will get the answer as 0 .19 and 44 this is the answer we have for but we have to give the answer with two decimal places so the answer would be 0 .19 and what about for part b at least how many days should the longest 30 so the least value the least value b x1 so what that means graph graphically, if you graph the normal distribution, there should be x1 here, and the area of this region would be 30%.

01:38 It can write as 0 .3...

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