A psychologist studied the time x (in seconds) it took a subject to complete a pencil and paper maze while in the presence of a floral scent. Suppose x has a normal distribution with mean 70 seconds and standard deviation 15 seconds. Find P(X<58)

you can play around with Z table stuff at

http://davidmlane.com/hyperstat/z_table.html

Another way.

Z = (score-mean)/SD = (58-70)15 = ?

Then 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 that the time it takes to complete the maze is less than 58 seconds (P(X < 58)), we can use the standard normal distribution.

Step 1: Standardize the value
To calculate probabilities using the standard normal distribution, we need to standardize the given value using the formula: z = (x - μ)/σ, where z is the standard score, x is the given value, μ is the mean, and σ is the standard deviation.

In this case:
x = 58 seconds
μ = 70 seconds
σ = 15 seconds

So, the standard score is: z = (58 - 70) / 15 = -0.8

Step 2: Look up the probability
Next, we need to find the probability associated with the standardized score using a standard normal distribution table or a calculator. The probability we are looking for is the area to the left of the standardized score (-0.8).

By looking up the z-score of -0.8 in a standard normal distribution table, we can find that the corresponding probability is approximately 0.2119.

Step 3: Interpret the result
Therefore, P(X < 58) is approximately 0.2119, or 21.19%.

So, there is a 21.19% chance that a subject will complete the maze in less than 58 seconds in the presence of a floral scent, according to the given normal distribution.