Question

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 2 decimal places.)

c. Find the population standard deviation σ if the population mean μ = 139. (Round "z" value to 3 decimal places and final answer to 2 decimal places.)

d. Find the population standard deviation σ if the population mean μ = 122. (Round "z" value to 3 decimal places and final answer to 2 decimal places.)

Answer #1

Solution :

x = 161

Using standard normal table,

P(Z > z) = 0.04

1 - P(Z < z) = 0.04

P(Z < z) = 1 - 0.04

P(Z < 1.751) = 0.96

z = 1.751

(a)

standard deviation = = 13

Using z-score formula,

= (x - z * ) = 161 - 1.751 * 13 = 138.24

Population mean = 138.24

(b)

standard deviation = = 24

Using z-score formula,

= (x - z * ) = 161 - 1.751 * 24 = 118.98

Population mean = 118.98

(c)

= 139

= (x - ) / z = (161 - 139) / 1.751 = 12.56

population standard deviation = = 12.56

(d)

= 122

= (x - ) / z = (161 - 122) / 1.751 = 22.27

population standard deviation = = 22.27

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 =
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 =
126 and standard deviation σ = 22. [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) = 0.410. (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
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 = 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 =
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...

Let X be normally distributed with mean μ =
4.3 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) = 0.0869. (Round "z" value
and...

Let X be normally distributed with mean μ = 3.4 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...

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 = 1.6 and standard
deviation σ = 2.7. [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...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 6 minutes ago

asked 13 minutes ago

asked 18 minutes ago

asked 46 minutes ago

asked 46 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago