The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50. What is the probability that a student uses more than 350 minutes?
1.2857
To find the probability that a student uses more than 350 minutes, we need to calculate the z-score for 350 minutes and then look up the corresponding probability from the standard normal distribution.
The formula for calculating the z-score is:
z = (x - μ) / σ
where:
- x is the value we are interested in (350 minutes in this case)
- μ is the mean of the normal distribution (500 minutes)
- σ is the standard deviation of the normal distribution (50 minutes)
Let's calculate the z-score for 350 minutes:
z = (350 - 500) / 50
= -150 / 50
= -3
Now, we need to find the probability associated with a z-score of -3. Using a standard normal distribution table or a calculator, we can find that the probability is approximately 0.0013.
Therefore, the probability that a student uses more than 350 minutes is approximately 0.0013 or 0.13%.
To find the probability that a student uses more than 350 minutes, we need to calculate the area under the normal distribution curve to the right of 350.
Here's how you can calculate it step by step:
Step 1: Standardize the value of 350 using the z-score formula:
z = (x - μ) / σ
Where:
x = the value we want to standardize (350 in this case)
μ = the mean of the distribution (500 in this case)
σ = the standard deviation of the distribution (50 in this case)
Using these values, we can calculate:
z = (350 - 500) / 50
= -150 / 50
= -3
Step 2: Look up the value of the standard normal distribution table to find the proportion of the area under the curve to the right of z = -3. You can either use a standard normal distribution table or a calculator that has the capability to calculate probabilities from the standard normal distribution.
The area to the right of z = -3 is the same as the area to the left of z = 3. From the standard normal distribution table, we find that the area to the left of z = 3 is approximately 0.9987.
Step 3: Subtract the result from 1 to find the probability that a student uses more than 350 minutes:
P(X > 350) = 1 - P(X ≤ 350)
= 1 - 0.9987
= 0.0013
So, the probability that a student uses more than 350 minutes is approximately 0.0013 or 0.13%.
Use z-scores.
Formula:
z = (x - mean)/sd
mean = 500
sd = 50
x = 350
Substitute the values into the formula and find z. Use a z-table to determine your probability.