Question

Suppose *X* is a normal random variable with mean
*μ* = 100 and standard deviation *σ* = 7. Find
*b* such that

* P*(100 ≤

HINT [See Example 3.] (Round your answer to one decimal
place.)

*b* =

Answer #1

Using standard normal conversion,

P(X < x) = P(Z < (x - ) / )

P(100 < X < b) = 0.3

P(X < b) - P(X < 100) = 0.3

P(Z < ( b - 100) / 7 ) - P(Z < (100 - 100) / 7 ) = 0.3

P(Z < ( b - 100) / 7 ) - P(Z < 0) = 0.3

P(Z < ( b - 100) / 7 ) - 0.5 = 0.3

P(Z < ( b - 100) / 7 ) = 0.8

From Z table, z-score for the probability of 0.8 is 0.8416

( b - 100) / 7 = 0.8416

**b = 105.9**

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.

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 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)

7. A normal random variable x has mean μ = 1.7
and standard deviation σ = 0.17. Find the probabilities of
these X-values. (Round your answers to four decimal
places.)
(a) 1.00 < X <
1.60
(b) X > 1.39
(c) 1.25 < X < 1.50
8. Suppose the numbers of a particular type of bacteria in
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approximately normally distributed, with a mean of 81 and a
standard deviation of 8. What...

Find the mean, μ, and standard deviation, σ, for a binomial
random variable X. (Round all answers for σ to three decimal
places.)
(a) n = 45, p = .50.
μ =
σ =
(b) n = 1, p = 0.25.
μ =
σ =
(c) n = 100, p = 0.75.
μ =
σ =
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μ =
σ =

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)

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= 48 and standard deviation σ = 6.2, find the following
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(a) P(x ≤ 60)
(b) P(x ≥ 50)
(c) P(50 ≤ x ≤ 60)

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