Given the mean = 40 and standard deviation = 5.31 find the probability that a value will fall below 34.
I know how to find the percentage of values that fall below 34. How do I get the probability?
Use the z-score table at the back of your text book : ) It reads 'Less than" for the probability so it will give you less than 34 once you have found the z score : )
I'm taking an online class and that isn't included in the z score table my professor attached...
Example: 5% = .05 probability
To find the probability that a value will fall below 34, you need to calculate the z-score and then use a standard normal distribution table or calculator to find the corresponding probability. Here are the steps to follow:
1. Calculate the z-score: The z-score measures how many standard deviations an individual value is away from the mean. It is calculated using the formula:
z = (x - μ) / σ
where x is the value in question, μ is the mean, and σ is the standard deviation.
In this case, x = 34, μ = 40, and σ = 5.31. Plugging in these values, we get:
z = (34 - 40) / 5.31 ≈ -1.13
2. Look up the probability: Once you have the z-score, you can use a standard normal distribution table or a calculator to find the corresponding probability. The standard normal distribution table provides the probabilities for various z-scores.
For a z-score of -1.13, you need to find the probability of getting a value less than -1.13. The table will provide the corresponding probability.
If you're using a calculator, you can use the cumulative distribution function (CDF) for a standard normal distribution to find this probability.
So, using either a standard normal distribution table or a calculator, you would look up the z-score of -1.13 and find the corresponding probability.