Question

The Acme Company manufactures widgets. The distribution of
widget weights is bell-shaped. The widget weights have a mean of 58
ounces and a standard deviation of 11 ounces.

Use the Standard Deviation Rule, also known as the Empirical
Rule.

Suggestion: sketch the distribution in order to answer these
questions.

a) 68% of the widget weights lie between and

b) What percentage of the widget weights lie between 25 and 69
ounces? %

c) What percentage of the widget weights lie above 36
? %

Answer #1

Let the random variable X is denoted as widget weight.

Given : The distribution of X is bell shaped with mean 58 and standard deviation 11.

i.e.

Empirical Rule or three sigma rule.

68.27% value lies within one standard deviation.

95.45% values lies within two standard deviation.

99.73 % value lies within three standard deviation.

i.e.

i.e.

Graph:

a) By empirical rule

**68% of the widget weight lie between 47 and 69
ounces**

b ) Required Percentage = P ( 25 < X < 69) = P ( 25 < X < 58) + P (58 <X < 69)

From graph

P(25 < X < 58 ) = 34.1% + 34.1%

P( 58 < X < 69) = 13.6%

Hence required probability is

P ( 25 < X < 69) = 34.1% + 34.1% + 13.6% = 81.8%

**81.8% percentage of widget weights lies between 25 and
69 ounces.**

**c)** Required Percentage = P ( X > 36)

= 1- P (X < 36)

By empirical rule 95.45% widget weight lies between 36 and 80.

Since the distribution is symmetric.

2.275% ( 1 -0.9545 = 0.455, 0.455/2 = 0.0275 ) widget weight below 36 and above 80.

Hence required percentage

P ( X > 36) = 1- 0.02275 = 0.97725 = 97.725%

**97.725 % widget weight lie above 36 ounces.**

The Acme Company manufactures widgets. The distribution of
widget weights is bell-shaped. The widget weights have a mean of 61
ounces and a standard deviation of 3 ounces. Use the Standard
Deviation Rule, also known as the Empirical Rule. Suggestion:
sketch the distribution in order to answer these questions.
a) 99.7% of the widget weights lie between and
b) What percentage of the widget weights lie between 58 and 70
ounces? %
c) What percentage of the widget weights lie...

The Acme Company manufactures widgets. The distribution of
widget weights is bell-shaped. The widget weights have a mean of 58
ounces and a standard deviation of 10 ounces.
Use the Standard Deviation Rule, also known as the Empirical
Rule.
Suggestion: sketch the distribution in order to answer these
questions.
a) 95% of the widget weights lie between and
b) What percentage of the widget weights lie between 48 and 78
ounces? %
c) What percentage of the widget weights lie above 28...

The Acme Company manufactures widgets. The distribution of
widget weights is bell-shaped. The widget weights have a mean of 56
ounces and a standard deviation of 6 ounces.
Use the Standard Deviation Rule, also known as the Empirical
Rule.
Suggestion: sketch the distribution in order to answer these
questions.
a) 95% of the widget weights lie between and
b) What percentage of the widget weights lie between 50 and 68
ounces? %
c) What percentage of the widget weights lie below 74...

The Acme Company manufactures widgets. The distribution of
widget weights is bell-shaped. The widget weights have a mean of 39
ounces and a standard deviation of 10 ounces.
Use the Standard Deviation Rule, also known as the Empirical
Rule.
Suggestion: sketch the distribution in order to answer these
questions.
a) 68% of the widget weights lie between ___ and ____
b) What percentage of the widget weights lie between 9 and 49
ounces?
c) What percentage of the widget weights...

The Acme Company manufactures widgets. The distribution of
widget weights is bell-shaped. The widget weights have a mean of 54
ounces and a standard deviation of 9 ounces.
Use the Empirical Rule, find
a) 68% of the widget weights lie between _____ and ______
b) What percentage of the widget weights lie between 27 and 63
ounces? _____ %
c) What percentage of the widget weights lie above 36 ? _____
%
Suggestion: sketch the distribution in order to answer...

The Acme Company manufactures widgets. The distribution of
widget weights is bell-shaped. The widget weights have a mean of 54
ounces and a standard deviation of 8 ounces. Use the 68-95-99.7
rule (also known as the Empirical Rule). Suggestion: sketch the
distribution in order to answer these questions. a) 99.7% of the
widget weights lie between and b) What percentage of the widget
weights lie between 46 and 78 ounces? % c) What percentage of the
widget weights lie below...

The Acme Company manufactures widgets. The distribution of
widget weights is bell-shaped. The widget weights have a mean of 55
ounces and a standard deviation of 9 ounces.
Use the Empirical Rule, also known as the 68-95-99.7 Rule. Do not
use Tables or Technology to avoid rounding errors.
Suggestion: sketch the distribution in order to answer these
questions.
a) 68% of the widget weights lie between ?
b) What percentage of the widget weights lie between 37 and 64
ounces? %...

The Acme Company manufactures widgets. The distribution of
widget weights is bell-shaped. The widget weights have a mean of 62
ounces and a standard deviation of 7 ounces.
Use the Standard Deviation Rule, also known as the Empirical
Rule.
Suggestion: sketch the distribution in order to answer these
questions.
a) 95% of the widget weights lie between a and b
b) What percentage of the widget weights lie between 55 and 76
ounces?
c) What percentage of the widget weights...

The Acme Company manufactures widgets. The distribution of
widget weights is bell-shaped. The widget weights have a mean of 38
ounces and a standard deviation of 4 ounces. Use the Standard
Deviation Rule, also known as the Empirical Rule. Suggestion:
sketch the distribution in order to answer these questions. a) 95%
of the widget weights lie between and b) What percentage of the
widget weights lie between 26 and 46 ounces? % c) What percentage
of the widget weights lie...

The Acme Company manufactures widgets. The distribution of
widget weights is bell-shaped. The widget weights have a mean of 63
ounces and a standard deviation of 6 ounces.
Use the Standard Deviation Rule, also known as the Empirical
Rule.
Suggestion: sketch the distribution in order to answer these
questions.
a) 99.7% of the widget weights lie between and
b) What percentage of the widget weights lie between 57 and 81
ounces? %
c) What percentage of the widget weights lie above 51...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 13 minutes ago

asked 22 minutes ago

asked 22 minutes ago

asked 48 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago