Question

The distribution of weights of a sample of 500 toddlers is
symmetric and bell-shaped.

According to the Empirical Rule, what percent of the weights will
lie between plus or

minus three sigmas (standard deviations) from the mean?

Group of answer choices

68%

34%

99.7%

95%

None of these

If a sample of toddlers has an estimated mean weight of 52
pounds and a standard

deviation of 4 pounds, then 95% of the toddlers have weights
between which two

values?

If a sample of toddlers has an estimated mean weight of 52
pounds and a standard

deviation of 4 pounds, then what percentage of toddlers weigh
between 44 and 56 pounds?

Group of answer choices

68%

34%

None of these

81.5%

47.5%

Group of answer choices

44 pounds and 60 pounds

40 pounds and 64 pounds

48 pounds and 56 pounds

None of these

48 pounds and 60 pounds

Answer #1

1)

99.7%

2)

mena = 52 , s= 4

95% of data falls within 2sd of mean

mena +/- sd

= 52 +/ - 2 *4

= 44 and 60

3)

Here, μ = 52, σ = 4, x1 = 44 and x2 = 56. We need to compute P(44<= X <= 56). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ

z1 = (44 - 52)/4 = -2

z2 = (56 - 52)/4 = 1

Therefore, we get

P(44 <= X <= 56) = P((56 - 52)/4) <= z <= (56 -
52)/4)

= P(-2 <= z <= 1) = P(z <= 1) - P(z <= -2)

= 0.8413 - 0.0228

= 0.8185

81.5%

The weights of loads hauled by a trucking company approximately
follow a bell-shaped (normal) frequency curve with a mean of 15
thousand pounds and a standard deviation of 4 thousand pounds. Note
that: 15 ± (1)(4) ==> 11 to 19; 15 ± (2)(4) ==> 7 to 23; 15 ±
(3)(4) ==> 3 to 27 . According to the empirical rule,
approximately __________ percent of loads weigh between 3 thousand
pounds and 27 thousand pounds.
Group of answer choices a)90 b)68...

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 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 with a mean of 44 ounces and a
standard deviation of 6 ounces. Using the Empirical Rule, answer
the following questions. Suggestion: Sketch the distribution.
a) 95% of the widget weights lie between ? and ?
b) What percentage of the widget weights lie between 38 and 56
ounces? %
c) What percentage of the widget weights lie below 62? %

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 9 ounces.
Use the Empirical Rule and a sketch of the normal 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 38 and 65
ounces? %
c) What percentage of the widget weights lie below 65
? %

The distribution of the weights of a sample of 1,400 cargo
containers is symmetric and bell-shaped. According to the Empirical
Rule, what percent of the weights will lie:
(a) Between 1formula38.mml and 1formula39.mml ?
Percentage of weights
%
(b1) Between 1formula40.mml and 1formula39.mml? (Round your
answer to 1 decimal place.)
Percentage of weights
%
(b2) Below 1formula38.mml? (Round your answer to 1 decimal
place.)
Percentage of weights
%

(01.06 LC)
The weight of laboratory grasshoppers follows a Normal
distribution, with a mean of 90 grams and a standard deviation of 2
grams. What percentage of the grasshoppers weigh between 86 grams
and 94 grams? (3 points)
99.7%
95%
68%
47.5%
34%

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...

A particular population, for which the frequency curve is
bell-shaped (normal), has a mean of μ=100 and a standard deviation
of σ=18. For samples of size n=36 consider the sampling
distribution of the sample mean ("xbar").
Note that 18 36=3 and that
100±(1)(3)⟹97 to 103
100±(2)(3)⟹94 to 106
100±(3)(3)⟹91 to 109
According to the empirical rule, approximately _____
percent of samples of size 36 will produce a sample mean between 97
and 103.
Group of answer choices
90
95
99.7...

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