The time that it takes for the next train to come follows a distribution with f(x) = 0.05 where x goes between 15 and 35 minutes. Round all numerical answers to two decimal places.

Answers:

a) mean = 2

b) Standard Deviation = 5.77

c) Probability that it takes 30 minutes for the next train to arrive = 0.75

d) Probability that the time taken will be between 25 and 30 minutes = 0.25

e) The 80th percentile = 31 minutes

f) The third quartile = 30 minutes

Explanations:

Check the attached files for the solvings

step-by-step explanation:

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.