The average middle-distance runner at a local high school runs the mile in 4.5 minutes, with astandard deviation of 0.3 minute. What is the probability that a runner will run the mile in less than 4 minutes?
Possible Answers:
A)7%B)3%C)5%D)4%
I know it's C, but I don't know how to get it.
z-score
z=(x-mu)/sigma
then look it up : ) on your tables
z=1.666
your table is a less than table so the value will be the correct percent.
To find the probability that a runner will run the mile in less than 4 minutes, we need to use the concept of z-scores and the standard normal distribution.
First, we need to calculate the z-score for a runner completing the mile in 4 minutes.
The z-score formula is given by:
z = (x - μ) / σ
where:
- x is the value we want to find the z-score for (in this case, 4 minutes)
- μ is the mean (average) of the distribution (4.5 minutes)
- σ is the standard deviation of the distribution (0.3 minutes)
Plugging in the values, we have:
z = (4 - 4.5) / 0.3
z = -1.67
Next, we need to find the probability associated with this z-score. We can use a standard normal distribution table or a calculator to find this probability.
Looking up the z-score of -1.67 in a standard normal distribution table, we find that the probability is approximately 0.0475.
However, we need to find the probability that a runner will run the mile in less than 4 minutes, so we need to find the area to the left of the z-score.
Since the standard normal distribution is symmetric around the mean (z = 0), we can subtract the probability obtained above from 0.5 (which represents the area to the right of the mean) to get the desired probability:
P(z < -1.67) = 0.5 - 0.0475 = 0.4525
Converting this to a percentage, we get approximately 4.525%. Therefore, the correct answer is D) 4%.