Final answer:
To find the probability of a skydiver being between 40 and 57 years of age, calculate the z-scores for these ages and use a z-table or calculator to find the corresponding probabilities. Then, subtract the smaller probability from the larger one to get the desired probability.
Step-by-step explanation:
The student has asked to calculate the probability that a skydiver will be between 40 to 57 years of age given a normal distribution with a mean of 49.3 years and a standard deviation of 11.8 years. To solve this, we will use the z-score formula which is (X - μ) / σ, where X is the value whose probability we want to find, μ is the mean, and σ is the standard deviation. First, we calculate the z-scores for 40 and 57 years.
Z1 for 40 years = (40 - 49.3) / 11.8 = -0.788
Z2 for 57 years = (57 - 49.3) / 11.8 = 0.652
Next, we look up these z-scores in a z-table or use a calculator with normal distribution functions to find the probabilities corresponding to these z-scores. Then, we can find the probability of a skydiver's age being between the z-scores by subtracting the smaller area from the larger one.
The probability that a skydiver will be between 40 to 57 years of age is therefore the difference in the probabilities at Z1 and Z2. This kind of calculation is frequently performed in statistics to find the likelihood of a value falling within a specific range in a normal distribution.