Question

Let *X* be normally distributed with mean *μ* =
4.1 and standard deviation *σ* = 2. **[You may find it
useful to reference the** z table**.]**

**a.** Find *P*(*X* > 6.5).
**(Round " z" value to 2 decimal places and final
answer to 4 decimal places.)**

**b.** Find *P*(5.5 *≤ X ≤* 7.5).
**(Round " z" value to 2 decimal places and final
answer to 4 decimal places.)**

**c.** Find *x* such that *P*(*X
>* *x*) = 0.0594. **(Round " z" value
and final answer to 3 decimal places.)**

**d.** Find *x* such that *P*(*x*
≤ *X* ≤ 4.1) = 0.4719. **(Negative value should be
indicated by a minus sign. Round " z" value and final
answer to 3 decimal places.)**

Answer #1

Here

a)

Required probability =

b)

Required probability =

c)

We wan to find 'x' such that P(X>x) = 0.0594

d)

We wan to find 'x' such that

Let X be normally distributed with mean μ = 3.3 and standard
deviation σ = 1.8. [You may find it useful to reference the z
table.]
a. Find P(X > 6.5). (Round "z" value to 2 decimal places and
final answer to 4 decimal places.)
b. Find P(5.5 ≤ X ≤ 7.5). (Round "z" value to 2 decimal places
and final answer to 4 decimal places.)
c. Find x such that P(X > x) = 0.0668. (Round "z" value and...

Let X be normally distributed with mean μ = 12
and standard deviation σ = 6. [You may find it
useful to reference the z table.]
a. Find P(X ≤ 0). (Round
"z" value to 2 decimal places and final
answer to 4 decimal places.)
b. Find P(X > 3).
(Round "z" value to 2 decimal places and final
answer to 4 decimal places.)
c. Find P(6 ≤ X ≤ 12).
(Round "z" value to 2 decimal places and final...

Let X be normally distributed with mean μ =
102 and standard deviation σ = 34. [You may find
it useful to reference the z
table.]
a. Find P(X ≤ 100).
(Round "z" value to 2 decimal places and final
answer to 4 decimal places.)
b. Find P(95 ≤ X ≤ 110).
(Round "z" value to 2 decimal places and final
answer to 4 decimal places.)
c. Find x such that P(X
≤ x) = 0.360. (Round "z" value and...

Let X be normally distributed with mean μ =
103 and standard deviation σ = 35. [You may find
it useful to reference the z
table.]
c. Find x such that P(X
≤ x) = 0.360. (Round "z" value and
final answer to 3 decimal places.)
d. Find x such that P(X
> x) = 0.790. (Round "z" value
and final answer to 3 decimal places.)

Let X be normally distributed with mean μ =
3,400 and standard deviation σ = 2,200. [You may
find it useful to reference the z
table.]
a. Find x such that P(X
≤ x) = 0.9382. (Round "z" value to 2
decimal places, and final answer to nearest whole
number.)
b. Find x such that P(X
> x) = 0.025. (Round "z" value to 2
decimal places, and final answer to nearest whole
number.)
c. Find x such that P(3,400...

Let X be normally distributed with mean μ =
2,800 and standard deviation σ = 900[You may find
it useful to reference the z table.]
a. Find x such that
P(X ≤ x) = 0.9382. (Round
"z" value to 2 decimal places, and final answer to nearest
whole number.)
b. Find x such that
P(X > x) = 0.025. (Round
"z" value to 2 decimal places, and final answer to nearest
whole number.)
c. Find x such that P(2,800 ≤...

Let X be normally distributed with mean μ = 2.5 and standard
deviation σ = 2. Use Excel to answer the following questions.
Find k such that P(k ≤ X ≤ 2.5) =
0.4943. Round your answer to 2 decimal places.

The random variable X is normally distributed. Also, it is known
that P(X > 161) = 0.04. [You may find it useful to reference the
z table.]
a. Find the population mean μ if the population standard
deviation σ = 13. (Round "z" value to 3 decimal places and final
answer to 2 decimal places.)
b. Find the population mean μ if the population standard
deviation σ = 24. (Round "z" value to 3 decimal places and final
answer to...

Suppose that the random variable x is normally distributed with
μ = 1,000 and standard deviation σ = 100.
Find each of the following probabilities. Round your z-score
calculations to 2 decimal places. Provide your probability answers
to 4 decimal places.
z-score
probability
P( x > 1257)
P( x < 1035)
P( x ≤ 700)
z-score
z-score
probability
P(1000 ≤ x ≤ 1200)
P(812 ≤ x ≤ 913)

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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