Question

For a normal distribution, find the percentage of data that are (a) Within 1 standard deviation of the mean __________ % (b) Between ?−3.5? μ − 3.5 σ and ?+2.5? μ + 2.5 σ ____________% (c) More than 2 standard deviations away from the mean _________%

Answer #1

From Normal distribution tables

(a) Within 1 standard deviation of the mean is 68.27%

P(Mean - SD < X < Mean +SD) = P(-1 < Z < +1) = 0.6827 = 68.27%

(b) Between ?−3.5? and ?+2.5? is 99.34%

P(Mean - 3.5 SD < X < Mean + 2.5 SD) = P(-3.5 < Z < 2.5) = P(Z < 2.5) - P(Z < -3.5) = 0.99379 - 0.00023 = 0.99356 = 99.34%

(c) More than 2 standard deviations away from the mean is 4.55%

1 - P(Mean - 2*SD < X < Mean + 2*SD) = 1 - P(-2 < Z < 2) = 1 - 0.9545 = 0.0455 = 4.55%

For a standard normal distribution, find the percentage of data
that are: a. within 1 standard deviation of the mean ____________%
b. between - 3 and + 3. ____________% c. between -1 standard
deviation below the mean and 2 standard deviations above the
mean

For a normal distribution, find a) the percentage of data that
is greater than 3 standard deviations above the mean and b) the
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1. Assume that x has a normal distribution with the
specified mean and standard deviation. Find the indicated
probability. (Round your answer to four decimal places.)
μ = 14.3; σ = 3.5
P(10 ≤ x ≤ 26)=?
2.Assume that x has a normal distribution with the
specified mean and standard deviation. Find the indicated
probability. (Round your answer to four decimal places.)
μ = 5.9; σ = 1.1
P(7 ≤ x ≤ 9)=?
3. Assume that x has a normal...

Find the indicated area under the curve of the standard normal
distribution; then convert it to a percentage and fill in the
blank.
About ______% of the area is between
zequals=minus−3.5
and
zequals=3.5
(or within 3.5 standard deviations of the mean).
About
nothing%
of the area is between
zequals=minus−3.5
and
zequals=3.5
(or within 3.5 standard deviations of the mean).

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specified mean and standard deviation. Find the indicated
probability. (Round your answer to four decimal places.)
μ = 4.4; σ = 2.2
P(3 ≤ x ≤ 6) =
b.) Consider a normal distribution with mean 34 and standard
deviation 2. What is the probability a value selected at random
from this distribution is greater than 34? (Round your answer to
two decimal places.)
c.) Assume that x has a normal...

a. Assume that x has a normal distribution with the
specified mean and standard deviation. Find the indicated
probability. (Round your answer to four decimal places.)
μ = 15.5; σ = 4.5 P(10 ≤ x ≤
26) =
b. Now, assume that x has a normal distribution with
the specified mean and standard deviation. Find the indicated
probability. (Round your answer to four decimal places.)
μ = 14.2; σ = 2.9 P(8 ≤
x ≤ 12) =
c. Now, assume...

1.Assume that x has a normal distribution with the specified
mean and standard deviation. Find the indicated probability. (Round
your answer to four decimal places.) μ = 8; σ = 6 P(5 ≤ x ≤ 14)
=
2. Assume that x has a normal distribution with the
specified mean and standard deviation. Find the indicated
probability. (Round your answer to four decimal places.)
μ = 14.4; σ = 4.2
P(10 ≤ x ≤ 26) =
3. Assume that x has...

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n equals=70, find the probability of a sample mean being greater
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1) For a sample of n equals=70, the probability of a sample mean
being greater than 218 if μ=217 and σ equals=3.5 is ______.
2) The sample mean (would/ would not) _____ be...

Assume that x has a normal distribution with the specified mean
and standard deviation. Find the indicated probability. (Round your
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=

The Standard Normal Distribution with a mean of 0 and a standard
deviation of 1 has been used to calculate areas under the normal
distribution curve. Originally, quality control analysts were
content to confine all data within +/- three
standard deviations from the mean. The Ford Motor Company in the
mid 1980s decided to try to confine all data within +/-
four standard deviations from the mean. Six Sigma,
the newest quality venture, is trying to confine all data within...

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