population mean of 110 and SD of 6, what is likelihood of having score of 100 0r lower
P(Z < -10/6) = 0.478
P=0.0478 is correct
To determine the likelihood of having a score of 100 or lower, we need to calculate the z-score and then use a standard normal distribution table or calculator to find the corresponding probability.
The z-score is a measure of how many standard deviations an observation is away from the mean. It can be calculated using the formula:
z = (x - μ) / σ
Where:
- x is the value we want to find the probability for (in this case, 100).
- μ is the mean of the population (110).
- σ is the standard deviation of the population (6).
Now let's calculate the z-score:
z = (100 - 110) / 6
z = -10 / 6
z ≈ -1.67
Once we have the z-score, we can find the corresponding probability using a standard normal distribution table or a calculator.
For a z-score of -1.67, the probability of having a score of 100 or lower can be found as the cumulative probability to the left of the z-score.
Using a standard normal distribution table, we can look up the cumulative probability for a z-score of -1.67, which is approximately 0.0475. This means that roughly 4.75% of the population is likely to have a score of 100 or lower.
Alternatively, you can use a calculator or statistical software that provides the option to calculate the cumulative probability directly. Just input the z-score (-1.67) and it will give you the corresponding probability.
Remember that probabilities are always between 0 and 1, so the result represents the likelihood as a decimal or as a percentage (4.75%).