If I selected one player at random what would be the probability of an NBA player in the Eastern conference being less than 6 feet tall? First calculate the z-score and then use the standard normal table to find the probability.
so, do you have a table of NBA players' heights? If so, just do what the exercise says.
When you get the missing data:
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
To find the probability of an NBA player in the Eastern conference being less than 6 feet tall, we need to calculate the z-score and then use the standard normal table.
1. Calculate the z-score:
The z-score measures how many standard deviations an individual value is from the mean of a distribution. In this case, we need to calculate the z-score for a player's height of less than 6 feet, given the mean and standard deviation of NBA player heights.
Let's assume the mean height of NBA players in the Eastern conference is μ = 6.5 feet, and the standard deviation is σ = 0.5 feet.
The formula for calculating the z-score is:
z = (x - μ) / σ
where x is the individual value, μ is the mean, and σ is the standard deviation.
For a height of less than 6 feet, the z-score would be:
z = (6 - 6.5) / 0.5 = -1
2. Use the standard normal table:
The standard normal table, also known as the Z-table, is a table that provides the probabilities associated with various z-scores. It can be used to find the probability of an event occurring within a certain range.
To find the probability of a z-score less than -1, we need to locate the corresponding value in the standard normal table. The table will give us the probability associated with that z-score.
Referring to the standard normal table, we find that the probability of a z-score less than -1 is approximately 0.1587.
Therefore, the probability of an NBA player in the Eastern conference being less than 6 feet tall is approximately 0.1587 or 15.87%.
Remember, these calculations are based on the given assumptions for mean and standard deviation. The actual values may vary in reality.