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Chapter 4: Q117E (page 268)

If a population data set is normally distributed, what isthe proportion of measurements you would expect to fallwithin the following intervals?

a.渭卤蟽b.渭卤2蟽c.渭卤3蟽

Short Answer

Expert verified

a. The proportion of measurements that fall in the interval is 68%

b.The proportion of measurements that fall in the interval is 95%

c.The proportion of measurements that fall in the interval is 100%

Step by step solution

01

Given Information

The population is normally distributed.

02

Calculating the proportion when μ±2σ

b.

From the property of normal distribution,

P渭-蟽<X<渭+蟽=P渭-蟽-渭蟽<X-渭蟽<渭-蟽-渭蟽=P-1<Z<1=PZ<1-PZ鈮�-1=0.84134-0.15866=0.68269饾啅0.68P渭-蟽<X<渭+蟽饾啅0.68

The proportion of measurements that fall within 1 standard deviation of the mean is approximately 68%.

03

Calculating the proportion when

P渭-2蟽<X<渭+2蟽=P渭-2蟽-渭蟽<X-渭蟽<渭-2蟽-渭蟽=P-2<Z<2=PZ<2-PZ鈮�-2=0.97725-0.02275=0.9545饾啅0.95P渭-2蟽<X<渭+2蟽饾啅0.95

The proportion of measurements that fall within 2 standard deviations of the mean is approximately95%.

04

Calculating the proportion when

c.

P渭-3蟽<X<渭+3蟽=P渭-3蟽-渭蟽<X-渭蟽<渭-3蟽-渭蟽=P-3<Z<3=PZ<3-PZ鈮�-3=0.99865-0.00135=0.9973饾啅1P渭-3蟽<X<渭+3蟽饾啅1

The proportion of measurements that fall within 3 standard deviations of the mean is approximately 100%.

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Most popular questions from this chapter

Suppose x is a normally distributed random variable with 渭= 11 and 蟽= 2. Find each of the following:

a)P(10鈮�蠂鈮�12)

b) P(6鈮�蠂鈮�10)

c)P(13鈮�蠂鈮�16)

d)P(7.8鈮�蠂鈮�12.6)

e)P(蠂鈮�13.24)

f)P(蠂鈮�7.62)

Compute the following:

a.7!3!(7鈭�3)!

b.(94)

c. (50)

d.(44)

e.(54)

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Descriptive Statistics: Rating

Variable Rating

Price

N

Mean

St.Dev

Minimum

Q

1

median

Q3

Maximum

IQ

R

Job

99

7.879

4.224

1

4

9

11

20

7

Partner

60

8.883

4.809

1

5

8

12

20

7
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