Question

find the indicated probabilities using the geometric distribution, the poisson distribution, or the binomial distribution. then determine if the events are unusual. if convenient, use the appropriate probability table or technology to find the probabilities.
a newspaper finds that the mean number of typographical errors per page is eight. find the probability that (a) exactly five typographical errors are found on a page, (b) at most five typographical errors are found on a page, and (c) more than five typographical errors are found on a page.
(a) p(exactly five typographical errors are found on a page) = 0.0916
(round to four decimal places as needed.)
(b) p(at most five typographical errors are found on a page) = 0.1912
(round to four decimal places as needed.)
(c) p(more than five typographical errors are found on a page) = 0.8088
(round to four decimal places as needed.)
which of the events are unusual? select all that apply.
a. the event in part (a) is unusual.
b. the event in part (b) is unusual.
c. the event in part (c) is unusual.
d. none of the events are unusual.

Explanation:

To determine if an event is unusual, we use the rule that an event with probability \( P < 0.05 \) is considered unusual.

Step 1: Analyze Part (a)

The probability for part (a) is \( P(\text{exactly five}) = 0.0916 \). Since \( 0.0916 > 0.05 \), this event is not unusual.

Step 2: Analyze Part (b)

The probability for part (b) is \( P(\text{at most five}) = 0.1912 \). Since \( 0.1912 > 0.05 \), this event is not unusual.

Step 3: Analyze Part (c)

The probability for part (c) is \( P(\text{more than five}) = 0.8088 \). Since \( 0.8088 > 0.05 \), this event is not unusual.

Since none of the events have a probability less than 0.05, none of the events are unusual.

Answer:

D. None of the events are unusual.