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A set of data has a normal distribution with a mean of 5.1 and a standard deviation of 0.9. Find the percent of data between 4.2 and 5.1.

A)about 68%
B)about 34%
C)about 16%
D)about 13.5%

User Spaceballs
by
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2 Answers

6 votes

Answer:

34%

Explanation:

User WalkingRandomly
by
7.5k points
1 vote

A set of data has a normal distribution with a mean of 5.1 and a standard deviation of 0.9. Find the percent of data between 4.2 and 5.1.

Answer: The correct option is B) about 34%

Proof:

We have to find
P(4.2<x<5.1)

To find
P(4.2<x<5.1), we need to use z score formula:

When x = 4.2, we have:


z = (x-\mu)/(\sigma)


=(4.2-5.1)/(0.9)=(-0.9)/(0.9)=-1

When x = 5.1, we have:


z = (x-\mu)/(\sigma)


=(5.1-5.1)/(0.9)=0

Therefore, we have to find
P(-1<z<0)

Using the standard normal table, we have:


P(-1<z<0)=
P(z<0) - P(z<-1)


=0.50-0.1587


=0.3413 or 34.13%

= 34% approximately

Therefore, the percent of data between 4.2 and 5.1 is about 34%

User Rei
by
9.0k points
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