Question

in a random survey, college students were asked, how often do you wear a seat - belt when riding in a car driven by someone else? the response frequencies appear in the table to the right. (a) construct a probability model. (b) would you consider it unusual to find a college student who never wears a seat - belt when riding in a car driven by someone else? (round to the nearest thousandth as needed.) (round to the nearest thousandth as needed.) (round to the nearest thousandth as needed.) would you consider it unusual to find a college student who never wears a seat - belt when riding in a car driven by someone else? no, because the probability of an unusual event is 0. yes, because p(never) < 0.01. yes, because 0.01 < p(never) < 0.10. no, because there were 112 people in the survey who said they never wear their seat - belt.
response frequency
never 112
rarely 302
sometimes 57
most of the time 1250
always 2399

Explanation:

Step1: Calculate total number of students

The total number of students is the sum of the frequencies in the table. So, $112 + 302+57 + 1250+239=1960$.

Step2: Calculate probability of a student who never wears a seat - belt

The number of students who never wear a seat - belt is 112. The probability $P$ (never) is given by the formula $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So, $P(\text{never})=\frac{112}{1960}\approx0.0571$.

Step3: Round the probability

Rounding 0.0571 to the nearest thousandth gives 0.057.

Step4: Determine if the event is unusual

An event is considered unusual if its probability is less than or equal to 0.05. Since $0.057>0.05$, the event of a student never wearing a seat - belt is not unusual.

Answer:

(Round to the nearest thousandth as needed) 0.057
(Round to the nearest thousandth as needed) 0.057
(Round to the nearest thousandth as needed) 0.057
No, because the probability of an unusual event is $0 < P\leq0.05$