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