Bell-Curve BellhopData & Chance · statistics and probability

A bellhop shaped like a bell curve: the normal distribution.

The Normal Distribution

The normal distribution. In MathBound, the free Algebra I adventure game, Bell-Curve Bellhop asks these problems, and the only way past is to solve them.

Part of More topics: taught by some textbooks beyond the usual course.

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10 questions, no sign-up, nothing saved. Climbs from the basics to harder questions.

What you will practice

The 68-95-99.7 Rule. Give the share of a normal distribution within 1, 2 or 3 standard deviations of the mean.

Worked examples

Made by the game’s own question engine. Try each one, then open its steps.

Example 1 · The 68-95-99.7 Rule

Weights

of

eggs

from

a

farm

are

normally

distributed

with

mean

58

grams

and

standard

deviation

4

grams.

About

99.7%

of

them

lie

in

which

interval?

$between$ $55$ $and$ $61$ $grams$
$between$ $58$ $and$ $70$ $grams$
$between$ $54$ $and$ $62$ $grams$
$between$ $46$ $and$ $70$ $grams$

Show the worked steps

$About$ $99.7%$ $of$ $a$ $normal$ $distribution$ $lies$ $within$ $3$ $standard$ $deviations$ $of$ $the$ $mean.$
$58 - 12 = 46$ $and$ $58 + 12 = 70.$

Answer: $between$ $46$ $and$ $70$ $grams$

Example 2 · The 68-95-99.7 Rule

In

a

normal

distribution,

about

what

percent

of

the

data

lie

within

2

standard

deviations

of

the

mean?

$99.7%$
$47.5%$
$95%$
$68%$

Show the worked steps

$The$ $68 - 95 - 99.7$ $rule:$ $about$ $68%$ $within$ $1$ $standard$ $deviation,$ $95%$ $within$ $2$ $and$ $99.7%$ $within$ $3.$
$So$ $about$ $95%$ $lie$ $within$ $2.$

Answer: $95%$

Example 3 · The 68-95-99.7 Rule

Lifetimes

of

a

kind

of

battery

are

normally

distributed

with

mean

400

hours

and

standard

deviation

30

hours.

About

what

percent

lie

between

400

and

460

hours?

$47.5%$
$95%$
$2.5%$
$97.5%$

Show the worked steps

$One$ $end$ $is$ $the$ $mean;$ $the$ $other$ $is$ $2$ $standard$ $deviations$ $away.$
$That$ $is$ $half$ $of$ $95% : 47.5%.$

Answer: $47.5%$

Where it is in your textbook

Textbook	Lessons
SpringBoard Algebra 1	37

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