rkld-445428415& nld-8&flushed-true3dld-4674232;&icent; MATH 1342.21420 Homework:

Question

rkld-445428415& nld-8&flushed-true3dld-4674232;&icent; MATH 1342.21420 Homework: Section 9.2-The Central Limit Theorem for Sample Mre Score: 0 of 1 pt 9 of 15 (7 complete) 9.2.12 HW Score: 46.67%, 7 of 15 pts Some sources report that the weights of full- term newbom babies have a mean of 6 pounds and a standard deviation of 1.2 pounds and are Normally distributed in the given outputs, the shaded areas (reported size of 4, and one uses a sample size of 9 Complete parts (a) and (b) below -Question Help as p-) represent the probability that the mean will be larger than 7.2 or smaller than 4.8. One of the outputs uses a sample Click the icon to view the outputs a. Which is which, and how do you know? Fture As forthe sample see nd Figure B is for the sample size of | | The standard error is smaller for forsample sizes, so when the ndl likely to be more than 1 2 pounds away from the mean Click and then click Check Answer Clear Al

Explanation / Answer

Ans:

Given that

mean=6

standard deviation=1.2

when n=4

standard error of mean=1.2/sqrt(4)=1.2/2=0.6

when n=9

standard error of mean=1.2/sqrt(9)=1.2/3=0.4

standard error is small for n=9,because as the n increases,standard error decreases.

For n=9

z(4.8)=(4.8-6)/0.4=-1.2/0.4=-3

z(7.2)=(7.2-6)/0.4=1.2/0.4=3

P(z<-3)+P(z>3)=0.0027

For n=4

z(4.8)=(4.8-6)/0.6=-1.2/0.6=-2

z(7.2)=(7.2-6)/0.6=1.2/0.6=2

P(z<-2)+P(z>2)=0.0455

So,figure with smaller area at tail ends(0.0027) will be for n=9.

As,standard error is small,test statistic is Less likely to be more than 1.2 pounds away from the mean.

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