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Darina [25.2K]
3 years ago
6

Toby's Trucking Company determined that on an annual basis the distance traveled per truck is normally distributed with a mean o

f 50.0 thousand miles and a standard deviation of 12.0 thousand miles.
a. What proportion of trucks can be expected to travel between 34.0 and 50.0 thousand miles in the year?

Mathematics
1 answer:
8_murik_8 [283]3 years ago
7 0

Answer:

0.4082

Step-by-step explanation:

Data

mean (\mu) = 50,000 miles

standard deviation (\sigma) = 12,000 miles

expected distance (X) = 34,000 miles

In the figure attached, standard normal distribution table can be seen. Z is computed as follows:

Z = \frac{X - \mu}{\sigma}{

Z = \frac{34000 - 50000}{12000}{

Z = -1.33{

In standard table, the area between 0 and -1.33 is the sem as between 0 and 1.33. So, the proportion of trucks is 0.4082

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For ∠2.

Since the given triangle is an isosceles triangle.

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For ∠4.

∠4 and ∠2 makes straight angle, and we know that the measure of straight angle is 180°.

So, we can frame this in equation form as;

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Substituting the values of of angle 2 to find angle 4 we get;

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Substituting the values of of angle 4 to find angle 5 we get;

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Thus the measure of ∠5 is 65°.

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The measure of ∠2 is 65°.

The measure of ∠3 is 50°.

The measure of ∠4 is 115°.

The measure of ∠5 is 65°.

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