M= 19.8 SD= 7.2
What is the probability of randomly selecting a student with a treadmill time greater than 25 minutes? In symbols, P(X > 25) = ?
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.
1
To find the probability of randomly selecting a student with a treadmill time greater than 25 minutes, we need to use the z-score formula and the standard normal distribution.
The z-score formula is given by:
z = (X - μ) / σ
where X is the given value (in this case, 25 minutes), μ is the mean (in this case, M = 19.8), and σ is the standard deviation (in this case, SD = 7.2).
First, we calculate the z-score:
z = (25 - 19.8) / 7.2 = 0.722
Next, we look up the z-score in the standard normal distribution table (also known as the Z-table) to find the corresponding probability.
The z-table provides the cumulative probability to the left of a given z-score. Since we want the probability of X being greater than 25 minutes (P(X > 25)), we need to find the area to the right of the z-score.
Looking up the z-score of 0.722 in the table, we find that the cumulative probability is 0.7669.
However, this gives us the probability of X being less than or equal to 25 minutes, so we subtract it from 1 to get the probability of X being greater than 25 minutes:
P(X > 25) = 1 - 0.7669 = 0.2331
Therefore, the probability of randomly selecting a student with a treadmill time greater than 25 minutes is approximately 0.2331.