Question

answer the question, considering an event to be \unusual\ if its probability is less than or equal to 0.05. 9) a multiple choice question has 18 possible answers, only one of which is correct. is it \unusual\ to answer a question correctly if a random guess is made? a) yes b) no 10) assume that a study of 300 randomly selected school bus routes showed that 274 arrived on time. is it \unusual\ for a school bus to arrive late? a) yes b) no 11) if you are told that a mystery person’s name begins with a consonant, would it be \unusual\ to guess the first letter of that person’s name? a) yes b) no 12) if you drew one card from a standard deck, would it be \unusual\ to draw an ace of hearts? a) yes b) no 13) assume that one student in your class of 28 students is randomly selected to win a prize. would it be \unusual\ for you to win? a) yes b) no

Explanation:

Question 9

Step1: Calculate probability of correct guess

The number of possible answers is 18, and only 1 is correct. So the probability \( P(\text{correct}) = \frac{1}{18} \approx 0.0556 \).

Step2: Compare with 0.05

Since \( 0.0556 > 0.05 \), the event is not unusual.

Step1: Calculate number of late buses

Total routes: 300, on - time routes: 274. So late routes \( = 300 - 274=26 \).

Step2: Calculate probability of late arrival

\( P(\text{late})=\frac{26}{300}\approx0.0867 \).

Step3: Compare with 0.05

Since \( 0.0867>0.05 \), the event is not unusual.

Step1: Determine number of consonants and letters

There are 26 letters in the alphabet, 5 vowels and \( 26 - 5 = 21 \) consonants.

Step2: Calculate probability of guessing correctly

If the name starts with a consonant, the probability of guessing the first letter \( P=\frac{1}{21}\approx0.0476 \).

Step3: Compare with 0.05

Since \( 0.0476\leq0.05 \), the event is unusual.

Answer:

B) No

Question 10