Summer Trip Length Did high gas prices keep Americans from hitting the road this past summer? In a nationwide survey of adults, one variable measured was how many days’ vacationers spent driving on the road on their longest trip. Consider the following (partial) probability distribution for the random variable X = the number of days for the longest car trip. X 4 5 6 7 8 Probability 0.10 0.20 0.25 0.3 0.15 a. Suppose the probability of 7 days is twice as likely as the probability of 8 days. Complete the probability distribution for X. Show your work. Note: the total probability provided was 0.55, leaving 0.45 for the two missing probabilities. With 7 days twice as likely as 8 days, we divide up the 0.45 in a 2 to 1 ratio, thus 0.30 for 7 days and 0.15 for 8 days. b. What is the expected number of days for the longest trip? Include symbol, value, and units.
Summer Trip Length Did high gas prices keep Americans from hitting the road this past summer? In a nationwide survey of adults, one variable measured was how many days’ vacationers spent driving on the road on their longest trip. Consider the following (partial) probability distribution for the random variable X = the number of days for the longest car trip. X 4 5 6 7 8 Probability 0.10 0.20 0.25 0.3 0.15 a. Suppose the probability of 7 days is twice as likely as the probability of 8 days. Complete the probability distribution for X. Show your work. Note: the total probability provided was 0.55, leaving 0.45 for the two missing probabilities. With 7 days twice as likely as 8 days, we divide up the 0.45 in a 2 to 1 ratio, thus 0.30 for 7 days and 0.15 for 8 days. b. What is the expected number of days for the longest trip? Include symbol, value, and units.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Problem 2: Summer Trip Length
Did high gas prices keep Americans from hitting the road this past summer? In a nationwide survey of
adults, one variable measured was how many days’ vacationers spent driving on the road on their longest
trip. Consider the following (partial) probability distribution for the random variable X = the number of
days for the longest car trip.
X 4 5 6 7 8
Probability 0.10 0.20 0.25 0.3 0.15
a. Suppose the probability of 7 days is twice as likely as the probability of 8 days. Complete the
probability distribution for X. Show your work.
Note: the total probability provided was 0.55, leaving 0.45 for the two missing probabilities.
With 7 days twice as likely as 8 days, we divide up the 0.45 in a 2 to 1 ratio, thus 0.30 for 7 days and
0.15 for 8 days.
b. What is the expected number of days for the longest trip?
Include symbol, value, and units.
E(X) = µ = 4(0.10) + 5(0.20) + 6(0.25) + 7(0.30) + 8(0.15) = 0.4 + 1 + 1.5 + 2.1
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