Chapter 6: Q. 105 (page 430)
condition To use a binomial distribution to approximate the count of successes in an SRS, why do we require that the sample size n be less than of the population size ?
The sample size n must be smaller than 10% of the population size N.
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.Essay errors Typographical and spelling errors can be either “nonword errors” or “word errors.” A nonword error is not a real word, as when “the” is typed as “teh.” A word error is a real word, but not the right word, as when “lose” is typed as “loose.” When students are asked to write a -word essay (without spell-checking), the number of nonword errors X has the following probability distribution:
| Value of X | 0 | 1 | 2 | 3 | 4 |
| Probability | 0.1 | 0.2 | 0.3 | 0.3 | 0.1 |
| Value of Y | 0 | 1 | 2 | 3 |
| Probability | 0.4 | 0.3 | 0.2 | 0.1 |
a) Find the mean and standard deviation of the difference in the number of errors made by a randomly selected student. Interpret each value in context.
(b) Challenge: Find the probability that a randomly selected student makes more word errors than nonword errors .
Total gross profits on a randomly selected day at Tim’s Toys follow a distribution that is approximately Normal with mean and standard deviation . The cost of renting and maintaining the shop is per day. Let profit on a randomly selected day, so . Describe the shape, center, and variability of the probability distribution of .
The time it takes Hattan to drive to work on a randomly selected day follows a distribution that is approximately Normal with mean minutes and standard deviation minutes. Once he parks his car in his reserved space, it takes more minutes for him to walk to his office. Let the total time it takes Hattan to reach his office on a randomly selected day, so . Describe the shape, center, and variability of the probability distribution of .
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 (in dollars) on a randomly selected ferry trip is shown here.
Part (a). Find . Interpret this result.
Part (b). Express the event “at least $20 is collected” in terms of Y. What is the probability of this event?
Where’s the bus? Sally takes the same bus to work every morning. Let X = the amount of
time (in minutes) that she has to wait for the bus on a randomly selected day. The
probability distribution of X can be modeled by a uniform density curve on the interval
from 0 minutes to8 minutes. Find the probability that Sally has to wait between 2 and 5
minutes for the bus.
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