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Chapter 6: Q. 7. (page 367)

Get on the boat! Refer to Exercise 3. Find the mean of Y. Interpret this value.

Short Answer

Expert verified

碌=19.35

Step by step solution

01

Step 1. Given information.

Money collected0510152025
Probability 0.020.050.080.160.270.42
02

Step 2. The mean of Y. 

The expected value (or mean) is calculated by multiplying each possibility y by its probability P(Y = y):

碌=危yP(Y=y)=0x0.02+5x0.05+10x0.08+15x0.16+20x0.27+25x0.42碌=19.35

The average amount of money collected on a random ferry trip is $19.35.

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Take a spin An online spinner has two colored regions_blue and yellow. According to the website, the probability that the spinner lands in the blue region on any spin is 0.80. Assume for now that this claim is correct. Suppose we spin the spinner 12 times and let X=the number of times it lands in the blue region.

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Get on the boat! A small ferry runs every half hour from one side of a large river to the other. The probability distribution for the random variable Y= money collected on a randomly selected ferry trip is shown here. From Exercise 7, 渭Y=$19.35.

(a) Find the median of Y.

(b) Compare the mean and median. Explain why this relationship makes sense based on the probability distribution.
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