John drives to work each morning and the trip takes an average of µ = 38 minutes. The
distribution of driving times is approximately normal with a standard deviation of σ = 5
minutes. For a randomly selected morning, what is the probability that John’s drive to
work will take less than 35 minutes?
You have to find a z-score.
35-38 divided by 5.
Now, that you have the z-value, use a table or a calculator to find the area under the normal curve to the left of your z-value. This is the probability that it will take him less than 35 minutes to get to work.
This is really a Statistics problem. Make sure your subject line says Statistics and you will get help a little faster.
0.6554
To find the probability that John's drive to work takes less than 35 minutes, we need to calculate the area under the normal distribution curve to the left of 35 minutes.
We can use the standard normal distribution to do this. To standardize the value of 35 minutes, we can use the z-score formula, which is:
z = (x - µ) / σ
where x is the value we're interested in (35 minutes), µ is the mean (38 minutes), and σ is the standard deviation (5 minutes).
Plugging in the values:
z = (35 - 38) / 5
z = -3 / 5
z = -0.6
Now, we can use a standard normal distribution table or a calculator to find the probability corresponding to a z-score of -0.6.
Looking up the z-score -0.6 in a standard normal distribution table, we find that the probability is approximately 0.2743.
Therefore, the probability that John's drive to work will take less than 35 minutes is approximately 0.2743 or 27.43%.
To find the probability that John's drive to work will take less than 35 minutes, we need to calculate the area under the normal curve to the left of 35 minutes.
Step 1: Standardize the value
To do this, we need to convert the given value of 35 minutes to a standard score (also known as z-score) using the formula:
z = (x - µ) / σ
where z is the standard score, x is the given value, µ is the mean, and σ is the standard deviation.
In this case, x = 35 minutes, µ = 38 minutes, and σ = 5 minutes. Plugging in these values, we get:
z = (35 - 38) / 5
z = -3 / 5
z = -0.6
Step 2: Find the probability
Once we have the standard score, we can use a standard normal distribution table or calculator to find the probability. The standard normal distribution has a mean of 0 and a standard deviation of 1.
Using the standard normal distribution table or calculator, we can find that the probability corresponding to a z-score of -0.6 is approximately 0.2743.
So, the probability that John's drive to work will take less than 35 minutes is approximately 0.2743, or 27.43%.