For a car traveling 30 mph in normal conditions, the distance required to brake to a stop is normally with a mean of 50 feet and a standard deviation of 8. you are traveling in a area at 30 mph and a car swerves into your path at a distance of 60 feet away. what is the probability that you will be able to brake to a stop in less than 60 feet?
60 = 50+10
so, it is 10/8 = 1.25 above the mean
Check you Z table to find P(Z<1.25)
To find the probability of being able to brake to a stop in less than 60 feet, we need to calculate the z-score and then use a standard normal distribution table.
Step 1: Calculate the z-score
The z-score can be calculated using the formula: z = (x - μ) / σ, where x is the distance, μ is the mean, and σ is the standard deviation.
In this case, x = 60 feet, μ = 50 feet, and σ = 8 feet.
z = (60 - 50) / 8
z = 10 / 8
z = 1.25
Step 2: Look up the z-score in the standard normal distribution table
Now, we need to find the area under the curve to the left of the z-score of 1.25 in the standard normal distribution table. This area represents the probability of the distance being less than 60 feet.
Looking up the z-score of 1.25 in the table, we find that it corresponds to an area of 0.8944.
Step 3: Calculate the probability
The probability of being able to brake to a stop in less than 60 feet is equal to the area under the curve to the left of the z-score, which is 0.8944 or 89.44%.
Therefore, there is a 89.44% probability that you will be able to brake to a stop in less than 60 feet.