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soldier1979 [14.2K]
2 years ago
14

According to the empirical (69-95-99.7) rule, if a random variable z has a standard normal distribution, then approximately 95%

Mathematics
1 answer:
Dmitry_Shevchenko [17]2 years ago
7 0

Using z-scores, it is found that the value of z is z = 1.96.

-----------------------------

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula, which for a measure X, in a distribution with mean \mu and standard deviation \sigma, is given by:  

Z = \frac{X - \mu}{\sigma}

  • It measures how many standard deviations the measure is from the mean.
  • Each z-score has an associated p-value, which is the percentile.

  • The normal distribution is symmetric, which means that the middle 95% is between the <u>2.5th percentile and the 97.5th percentile</u>.
  • The 2.5th percentile is Z with a p-value of 0.025, thus Z = -1.96.
  • The 97.5th percentile is Z with a p-value of 0.975, thus Z = 1.96.
  • Thus, the value of Z is 1.96.

A similar problem is given at brainly.com/question/16965597

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#9 and #10<br> Please show work
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Answer:

Part 9) The number of items on Emily's grocery list is 5 and the number of items on Bobby's grocery list is 13

Part 10) The height of the taller bookshelf is 4 feet and the height of the shorter bookshelf is 1 foot

Step-by-step explanation:

Part 9)

Let

x ----> number of items on Emily's grocery list

x ----> number of items on Bobby's grocery list

we know that

y=2x+3 ----> equation A

x=y-8 ----> equation B

Solve by substitution

Substitute equation A in equation B

x=(2x+3)-8

solve for x

x=2x-5

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Find the value of y

y=2(5)+3=13

therefore

The number of items on Emily's grocery list is 5 and the number of items on Bobby's grocery list is 13

Part 10)

Let

x ----> the height of the taller bookshelf in feet

y ----> the height of the shorter bookshelf in feet

we have

x=5y-1 ----> equation A

Remember that

1\ ft=12\ in

To convert inches to feet divide by 12

so

60\ in=60/12=5\ ft

x+y=5 ----> equation B

Solve the system by substitution

substitute equation A in equation B

(5y-1)+y=5

solve for y

5y+y=5+1

6y=6

y=1\ ft

Find the value of x

x=5(1)-1=4\ ft

therefore

The height of the taller bookshelf is 4 feet and the height of the shorter bookshelf is 1 foot

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Answer:

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Step-by-step explanation:

Step 1: Set up equation

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Step 2: Solve

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x = 35

Step 3: Plug in

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And we have our answer!

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Answer:

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Step-by-step explanation:

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