### Problem 9 assign 4 RStudio The duration of a human\'s pregnancy is known to

Question

### Problem 9 assign 4 RStudio
The duration of a human's pregnancy is known to have a normal distribution with mean 40 weeks and standard deviation 1 week, but it has been shortened by a week with the same standard deviation in the United States, according to a report published in a recent year.

a) A baby was born yesterday, and his gestation period was in the 70th percentile of the normal distribution with mean 39 and standard deviation 1. What percentile would this be in the old days?
  
```{r}
#include solution in R
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b) Find the probability that the duration of a pregnancy was 37 to 40 weeks in 2015
  
```{r}
#include solution in R
```

Explanation / Answer

Ans:

a)

70th percentile means that

P(Z<=z)=0.7

z=0.52

z=0.52=(x-39)/1

x=39+0.52=39.52

use qnorm(0.7,39,1),it will give x value 39.52

Now with old distribution:

z=(39.52-40)/1

z=-0.48

P(z<-0.48)=0.3156

use pnorm(39.52,40,1),it will give 0.3156

31.56th percentile

b)mean=39,std dev=1

z(37)=(37-39)/1=-2

z(40)=(40-39)/1=1

P(-2<=z<=1)=P(z<=1)-P(z<=-2)=0.8413-0.0228=0.8186

use pnorm(40,39,1)-pnorm(37,39,1),it will give 0.8186

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