Let x be a continuous random variable that is normally distributed with a mean of 65 and a standard deviation of 15. Find the probability that x assumes a value less than 44.
To find the probability that x assumes a value less than 44, we need to calculate the cumulative probability up to 44 using the given mean and standard deviation.
Step 1: Standardize the value 44 using the z-score formula:
z = (x - mean) / standard deviation
z = (44 - 65) / 15
z = -21 / 15
z ≈ -1.4
Step 2: Use a standard normal distribution table or a calculator to find the cumulative probability associated with the z-value -1.4.
Looking up the z-value -1.4 in the z-table, we find that the cumulative probability is approximately 0.0808.
Therefore, the probability that x assumes a value less than 44 is approximately 0.0808 or 8.08%.
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.