Question

Rural Speed Limits Rural speed limits for all 50 states are indicated below. 60 mph 65 mph 70 mph 75 mph 1 (HI) 18 18 13 Choose one state at random. Find the probability that its speed limit is a. 60 or 70 miles per hour b. Greater than 65 miles per hour c. 70 miles per hour or less

Answer 1

`P(60mph\ or\ 70mph) = 0.38`

`P(x>65mph) = 0.62`

`P(x \le 70mph) = 0.74`

Explanation:

Given

Speed Limits --- States

60 mph ---------- 1

65 mph ----------- 18

70 mph ----------- 18

75 mph ---------- 13

Total -------------- 50

Solving (a): Probability of 60mph or 70mph

This is represented as:

`P(60mph\ or\ 70mph)`

We only consider states with speed limits of 60 and 70mph.

So, we have:

`P(60mph\ or\ 70mph) = P(60mph) + P(70mph)`

`P(60mph\ or\ 70mph) = (1)/(50) + (18)/(50)`

Take L.C.M

`P(60mph\ or\ 70mph) = (1+18)/(50)`

`P(60mph\ or\ 70mph) = (19)/(50)`

`P(60mph\ or\ 70mph) = 0.38`

Solving (b): Greater than 65mph

This is represented as:

`P(x>65mph)`

We only consider states with speed limits of 70 and 75mph.

So, we have:

`P(x>65mph) = P(70mph) + P(75mph)`

This gives:

`P(x>65mph) = (18)/(50) + (13)/(50)`

Take L.C.M

`P(x>65mph) = (18+13)/(50)`

`P(x>65mph) = (31)/(50)`

`P(x>65mph) = 0.62`

Solving (c): 70mph or less

This is represented as:

`P(x \le 70mph)`

We only consider states with speed limits of 60, 65 and 70mph.

So, we have:

`P(x \le 70mph) = P(60mph) + P(65mph) + P(70mph)`

This gives:

`P(x \le 70mph) = (1)/(50) + (18)/(50) + (18)/(50)`

Take L.C.M

`P(x \le 70mph) = (1+18+18)/(50)`

`P(x \le 70mph) = (37)/(50)`

`P(x \le 70mph) = 0.74`