Question

The survey belo w was conducted among high school students aged 16 or older for the purpose of investigating seat belt use. The table represents "percentages" ys use when drving Do not always use when driving Always Do not always Always Do not always use when use when use when use when passenger passenger passenger Characteristic passenger Total 3.4 37.6 38.4 Age (years) 16 17 218 3.2 3.6 3.6 36.1 38.4 38.6 38.2 38.1 394184 36 22.5 19.9 If one student is selected at random from this population, what is the probability that the student selected: 1. Always uses a seatbelt when driving and always uses a seatbelt when a passenger. 2. Always uses a seatbelt when driving but not always when a passenger, given they are 18 or older? oes not always use a seatbelt when driving and always does when a passenger, knowing they are 16? Always wears a seatbelt when driving? Does not always wear a seatbelt when driving and is 17 years old? 3. D 4. 5.

Answer 1

Consider the following table:

	Always use when driving		Do not always use when driving
	Always use when passenger	Do not always use when passenger	Always use when passenger	Do not always use when passenger	Total
Total	38.4	20.6	3.4	37.6	100
Age (years)
16	38.2	22.5	3.2	36.1	100
17	38.1	19.9	3.6	38.4	100
>18	39.4	18.4	3.6	38.6	100

1. Look at Total row. Out of all 100%, only 38.4% students always use a seatbelt when driving and always use a seatbelt when a passenger. Therefore:

P(always uses a seatbelt when driving and always uses a seatbelt when a passenger) = 38.4% = 0.384

2. Given they are 18 or older means, look at >18 row. Out of all 100% 18 or older students, only 18.4% students always use a seatbelt when driving but not always use a seatbelt when a passenger. Therefore:

P(always uses seatbelt when driving but not always uses seatbelt when a passenger|>18) = 18.4% = 0.184

3. Knowing they are 16 means look at 16 row. Out of all 100% 16 year old students, only 3.2% students do not always use a seatbelt when driving but always use a seatbelt when a passenger. Therefore:

P(do not always use seatbelt when driving but always uses seatbelt when a passenger|16) = 3.2% = 0.032

4. Look at Total row. Out of all, 38.4+20.6= 59% wears a seatbelt when driving. Therefore:

P(wears a seatbelt when driving) = 59% = 0.59