Final answer:
The student's question pertains to calculating probabilities for golf scores using a normal distribution in statistics, by finding z-scores and referencing a standard normal distribution table.
Step-by-step explanation:
The student's question involves understanding and calculating probabilities based on a normal distribution, which is a concept in statistics, a branch of mathematics. To answer this question, we use the given mean and standard deviation to determine the z-scores for the desired range of golf scores, and then translate these z-scores into probabilities using a standard normal distribution table or a graphing utility.
For the probability of scoring between 66 and 70 with a mean of 68 and a standard deviation of three:
- Calculate the z-scores for 66 and 70.
- Reference a standard normal distribution table or use a graphing utility to find the probabilities corresponding to these z-scores.
- Subtract the probability of scoring less than 66 from the probability of scoring less than 70 to get the probability of a score between 66 and 70.
Similarly, to find the probability of a golfer scoring less than 65:
- Calculate the z-score for 65.
- Use the standard normal distribution table or a graphing utility to find the corresponding probability.