NT Trucking Company determined that on an annual basis the d

NT Trucking Company determined that on an annual basis the distance travelled per truck is normally distributed with the mean of 100,000 kilometres and a standard deviation of 20,000 kilometres.

i. What proportion of trucks can be expected to travel between 80,000 and 120,000 kilometres in the year?
ii. What percentage of trucks can be expected to travel either below 60,000 or above 140,000 kilometres in the year?
iii. How many kilometres will be travelled by at least 80 percent of the trucks?

Solution

i. What proportion of trucks can be expected to travel between 80,000 and 120,000 kilometres in the year?

P(80,000 <X< 120,000)

=P((80000-100000)/20000 <(X-mean)/s <(120000-100000)/20000 )

=P(-1<Z<1)

=0.6827 (from standard normal table)

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ii. What percentage of trucks can be expected to travel either below 60,000 or above 140,000 kilometres in the year?

P(X<60,000 or X>140,000)

= P(Z<(60000-100000)/20000) + P(Z>(140000-100000)/20000)

=P(Z<-2) + P(Z>2)

=0.0455 (from standard normal table)

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iii. How many kilometres will be travelled by at least 80 percent of the trucks?

P(X<c) =0.8

--> P(Z<(c-100000)/20000) = 0.8

--> (c-100000)/20000 = 0.84 (from standard normal table)

So c= 100000+ 0.84*20000 =116800