Final answer:
To find the requested probabilities for a normal distribution with a mean of 73 and a standard deviation of 1.2, calculate z-scores for the given values and look up the corresponding probabilities using a z-table or a statistical calculator.
Step-by-step explanation:
The question refers to a normally distributed random variable X that is defined as X ~ N(73, 1.2).
To find the given probabilities, we need to use the properties of the normal distribution. Specifically:
- P(X > 74.5): Calculate the z-score for 74.5 and use the z-table or a calculator's normal distribution function to find the probability that X takes a value greater than 74.5.
- P(72.7 < X < 73.9): Calculate z-scores for both values and find the probability that X lies between them.
- P(72.7 < X < 74.5): Similar to the previous, calculate the z-scores for both values and find the probability that X is in this interval.
All these probabilities can be determined by looking up the corresponding areas under the normal distribution curve or by using statistical software/calculators.