the breaking distance of a Honda CRV can be approximated by a normal distribution, where the mean is 53 meters and the standard deviation is 3.8 meters. Let x be a random variable that represents a braking distance. Find the probability that a randomly selected braking distance is less than 49 meters
Use z-scores.
Formula:
z = (x - mean)/sd
With your data:
z = (49 - 53)/(3.8)
I'll let you finish the calculation.
Once you find the z-score, use a z-table to determine your probability. (Remember that the problem is asking for "less than" 49 meters.)
To find the probability that a randomly selected braking distance is less than 49 meters, we need to calculate the area under the normal distribution curve to the left of 49.
First, let's calculate the z-score for the value of 49 meters using the formula:
z = (x - μ) / σ
where:
x = value of the random variable (49 meters)
μ = mean (53 meters)
σ = standard deviation (3.8 meters)
z = (49 - 53) / 3.8
z = -1.05
Once we have the z-score, we can use a standard normal distribution table or a statistical calculator to find the probability corresponding to that z-score.
Using a standard normal distribution table, we look up the probability associated with a z-score of -1.05. We find that the probability is approximately 0.148.
Therefore, the probability that a randomly selected braking distance is less than 49 meters is approximately 0.148, or 14.8%.