Question

Given a normal distribution with μ=53 and σ=3.

a. What is the probability that X>49? P(X>49)=_____ (Round to four decimal places as needed.)

b. What is the probability thatX<47? P(X<47)equals=_____ (Round to four decimal places as needed.)

c. For this distribution, 7% of the values are less than what X-value? X=_____ (Round to the nearest integer as needed.)

d. Between what two X-values (symmetrically distributed around the mean) are 80% of the values? For this distribution, 80% of the values are between X=_____ and X=_____ (Round to the nearest integer as needed.)

Answer #1

Given a normal distribution with μ=100 and σ=10, complete parts
(a) through (d).
a. What is the probability that X>80?
(Round to four decimal places as needed.)
b. What is the probability that X<95?
(Round to four decimal places as needed.)
c. What is the probability that X<75 or X>110?
(Round to four decimal places as needed.)
d. 80% of the values are between what two X-values
(symmetrically distributed around the mean)?
(Round to two decimal places as needed.)

Given a normal distribution with μ=100 and σ=8, and given you
select a sample of n equals=16, complete parts (a) through
(d).
a. What is the probability that X is less than 95?
P(X<95)
(Type an integer or decimal rounded to four decimal places as
needed.)
b. What is the probability that X is between 95 and 97.5?
P(95<X<97.5)
(Type an integer or decimal rounded to four decimal places as
needed.)
c. What is the probability that X is above...

Suppose x has a distribution with μ = 53 and σ = 2.
Yes, the x distribution is normal with mean μ x = 53
and σ x = 0.5.
Find P(49 ≤ x ≤ 54).

X has a normal distribution with the given mean and
standard deviation. Find the indicated probability. (Round your
answer to four decimal places.)
μ = 39, σ = 20, find
P(32 ≤ X ≤ 49)

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 = 49; σ = 14
P(40 ≤ x ≤ 47) =

Given a normal distribution with Mean of 100 and Standard
deviation of 10, what is the probability that
between what two X values (symmetrically distributed around the
mean) are 80% of the values?

A population of values has a normal distribution with μ=137.5
and σ=14.4. A random sample of size n=142
is drawn.
Find the probability that a single randomly selected value is
between 136 and 140.6. Round your answer to four decimal
places.
P(136<X<140.6)=
Find the probability that a sample of size n=142 is randomly
selected with a mean between 136 and 140.6. Round your answer
to four decimal places.
P(136<M<140.6)=

A population of values has a normal distribution with μ=110.1
and σ=57.6. A random sample of size n=183
is drawn.
Find the probability that a single randomly selected value is
between 117.3 and 122.9. Round your answer to four decimal
places.
P(117.3<X<122.9)=
Find the probability that a sample of size n=183 is randomly
selected with a mean between 117.3 and 122.9. Round your answer
to four decimal places.
P(117.3<M<122.9)=

Suppose x has a distribution with μ = 80 and
σ = 11.
Find P(76 ≤ x ≤ 81). (Round your answer to
four decimal places.)

Suppose x has a distribution with μ = 84 and
σ = 11.
Find P(80 ≤ x ≤ 85). (Round your answer to four
decimal places.)

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