Question

Suppose the random variable X follows a normal distribution with mean μ=55and standard deviation σ=10.

Calculate each of the following.

In each case, round your response to at least 4 decimal places.

a) P(X<41)

b) P(X>64)

c)P(50<X<70)

Answer #1

Suppose the random variable X follows a normal
distribution with mean μ=50and standard deviation σ=10.
Calculate each of the following.
In each case, round your response to at least 4 decimal
places.
a) P(X<41)=
b) P(X>61)=
c) P(45<X<65)=

Suppose the random variable X follows a normal distribution with
mean μ=52 and standard deviation σ=10.
Calculate each of the following.
In each case, round your response to at least 4 decimal
places.
a) P(X < 41) =
b) P(X > 61) =
c) P (47 < X < 67) =

X is a normal random variable with mean μ and standard
deviation σ. Then P( μ− 1.2 σ ≤ X ≤ μ+ 1.9 σ) =?
Answer to 4 decimal places.

Suppose X is a normal random variable with mean
μ = 100 and standard deviation σ = 7. Find
b such that
P(100 ≤ X ≤
b) = 0.3.
HINT [See Example 3.] (Round your answer to one decimal
place.)
b =

11. 7 & 8 (S 7.2) Suppose the random variable X
follows a normal distribution with mean ?=103and
standard deviation ?=25.
Calculate each of the following.
In each case, round your response to at least 2 decimal
places.
a) Calculate the location of the 86th percentile on the
distribution of X.
b) Calculate the location of the 31st percentile on the
distribution of X.

Given that x is a normal variable with mean μ
= 51 and standard deviation σ = 6.5, find the following
probabilities. (Round your answers to four decimal places.)
(a) P(x ≤ 60)
(b) P(x ≥ 50)
(c) P(50 ≤ x ≤ 60)

Given that x is a normal variable with mean μ
= 48 and standard deviation σ = 6.2, find the following
probabilities. (Round your answers to four decimal places.)
(a) P(x ≤ 60)
(b) P(x ≥ 50)
(c) P(50 ≤ x ≤ 60)

Given that x is a normal variable with mean μ
= 43 and standard deviation σ = 6.5, find the following
probabilities. (Round your answers to four decimal places.)
(a) P(x ≤ 60)
(b) P(x ≥ 50)
(c) P(50 ≤ x ≤ 60)

Given that x is a normal variable with mean μ = 43 and standard
deviation σ = 6.7, find the following probabilities. (Round your
answers to four decimal places.) (a) P(x ≤ 60) (b) P(x ≥ 50) (c)
P(50 ≤ x ≤ 60)

Given that x is a normal variable with mean μ = 42 and standard
deviation σ = 6.1, find the following probabilities. (Round your
answers to four decimal places.) (a) P(x ≤ 60) (b) P(x ≥ 50) (c)
P(50 ≤ x ≤ 60)

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