Question

*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.

Answer #1

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 =

Answer the question for a normal random variable x with
mean μ and standard deviation σ specified below.
(Round your answer to one decimal place.)
μ = 38 and σ = 8.
Find a value of x that has area 0.01 to its right.

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) =

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=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)

given normal random variable x with mean μ= 57.1 and standard
deviation σ=13.2, what is P (46 < x̄ < 69)
for a sample of size n= 16?

A normal random variable x has mean μ = 1.6 and standard
deviation σ = 0.19. Find the probabilities of these X-values.
(Round your answers to four decimal places.)
1.00 < X < 1.20
X > 1.37
1.35 < X < 1.50

A normal random variable x has mean μ = 1.7 and standard
deviation σ = 0.16. Find the probabilities of these X-values.
(Round your answers to four decimal places.)
(a) 1.00 < X < 1.50 =
(b) X > 1.35 =
(c) 1.45 < X < 1.50 =

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)

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