Answer:
Step-by-step explanation:
Hello!
The variable of interest is
X: speed of a vehicle along a stretch of I-10 (mph)
This variable has a normal distribution with mean μ= 81 mph and a standard deviation σ= 8 mph.
The speed limit in the said stretch is 65 mph.
You need to calculate the probability of picking a car at random and its speed be at most 65 mph, symbolically:
P(X≤65)
To reach the probability, you need to use the standard normal distribution. To standardize the value fo X you have to subtract the value of μ and then divide it by σ:
P(Z≤(65-81)/8)= P(Z≤-2.00)
Now you look for the corresponding probability in the table of the standard normal distribution, since the value is negative you have to use the left entry. The integer and first decimal numbers are in the first column and the second decimal number is in the first row.
P(Z≤-2.00)= 0.0228
I hope it helps!
