Question

question 8
1 pts
the random variable x is known to be uniformly distributed between 1.88 and 6.54. compute the standard deviation of x.
1.345
3.295
1.180
2.330
2.052
4.210
question 9
1 pts
the scheduled commuting time on the silver star rail road from trenton, nj to new york city is 68 minutes. suppose that the actual commuting time is uniformly distributed between 56 and 72 minutes. what is the probability that train will arrive in new york late? (that is, the trip takes longer than the scheduled commuting time.)
0.250
0.235
0.063
1.063
0.750
4.000
question 10
1 pts

Explanation:

Question 8

Step1: Recall uniform distribution SD formula

For a uniform distribution on \([a, b]\), the standard deviation \(\sigma = \frac{b - a}{\sqrt{12}}\). Here, \(a = 1.88\), \(b = 6.54\).

Step2: Calculate \(b - a\)

\(b - a = 6.54 - 1.88 = 4.66\)

Step3: Compute standard deviation

\(\sigma = \frac{4.66}{\sqrt{12}} \approx \frac{4.66}{3.4641} \approx 1.345\)

Step1: Recall uniform probability formula

For \(X \sim \text{Uniform}(a, b)\), \(P(X > k) = \frac{b - k}{b - a}\) if \(k\) is in \([a, b]\). Here, \(a = 56\), \(b = 72\), \(k = 68\) (scheduled time).

Step2: Calculate \(b - k\) and \(b - a\)

\(b - k = 72 - 68 = 4\), \(b - a = 72 - 56 = 16\)

Step3: Compute probability

\(P(X > 68) = \frac{4}{16} = 0.250\)

Answer:

1.345

Question 9