Question

QUESTION 1

Given a normal distribution with μ = 50 and σ = 4, what is the
probability that

a) P (X > 43)

b) P (X<42)

c) 5% of the values are less than what X value

QUESTION 2

Toby’s truck company determined that on an annual basis the
distance traveled per truck is normally distributed with a mean of
50 thousand miles and a standard deviation of 12 thousand
miles

REQUIRED:

a)what proportion of trucks can be expected to travel between 34 to
50 thousand miles in the year?

b) What percentage of trucks can be expected to travel either below
30 thousand miles or above 60 thousand miles in the year?

Answer #1

**Question 1)**

We have

We know that to convert a normal distribution to a standard normal distribution, we use

a)

We need

=0.9599 (From the Z table)

b)

We need

= 0.0228 (From the Z table)

c) To compute this, we need to find such that

From the Z table

Therefore 5% of the values are less than 43.44

**Question 2)**

Let all the values be represented in 000'

We have

a)

We need to find

= 0.4082 (From the Z table)

Therefore 40.82% of trucks can be expected to travel between 34 to 50 thousand miles in the year

b)

We need to find

=0.0475+0.2033

= 0. 2508

Therefore 25.08 % of trucks can be expected to travel either below 30 thousand miles or above 60 thousand miles in the year

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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 a normal distribution with
μ=50
and
σ=5,
and given you select a sample of
n=100,
complete parts (a) through (d).
a. What is the probability that X is less than 49?
P(X<49)=
b. What is the probability that X is between 49 and 51.5?
P(49<X<51.5)=
c. What is the probability that X is above 50.9?
P(X>50.9)=
d. There is a 30% chance that X is above what value?
X=

For a normal distribution where μ= 100 and σ= 10, What is the
probability of:
a. P(X>80)
b. P(95<X<105)
c. P(X<50)
d. P(X>100)
e. P(X<90 y X>110)
f. P(X>135)

Given a normal distribution with μ= 101 and σ = 20, and given
you select a sample of equals =16
What is the probability that X is above 102.6?
P (X > 102.6) =

Q2. Given a normal distribution with μ = 30 and σ =
6,
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1- the normal curve area to the right of x = 17 [Hint:
P(X>17)]
2-the normal curve area to the left of x = 22 [Hint:
P(X<22)]
3-the normal curve area between x = 32 and x =
41[Hint: P(32<X<41)];
4-the value of x that has 80% of the normal curve area
to the left [Hint: P(X<k)=0.8];

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