Question

Show all formulae and work. Draw the normal distribution when needed. 3. If the scores for a test have a mean of 79 and a standard deviation of 10.8, find the probability that a score will fall below 65.

Answer 1

To find the probability that a score will fall below 65, you can use the z-score formula and then refer to a standard normal distribution table or calculator to find the probability associated with that z-score.

Where:

X is the value you want to find the probability for (in this case, 65).

μ is the mean (given as 79).

σ is the standard deviation (given as 10.8).

After calculating the z-score for 65, you can look up the corresponding probability from a standard normal distribution table or use a calculator or software to find that the probability is approximately 0.097, or 9.7%.