Final answer:
To find probabilities for a normal distribution with a given mean and standard deviation, we can use the z-score formula and a z-table. For X less than 47, the probability is approximately 0.2743. For X between 47 and 49.5, the probability is approximately 0.1859. For X above 51.1, the probability is approximately 0.4129. There is no information provided to calculate the probability of X being a specific value like 35%.The correct option is D, There is a 35% chance.
Step-by-step explanation:
When dealing with a normal distribution, we can use the z-score formula to find probabilities. The formula is z = (X - µ) / σ, where X is the value we are interested in, µ is the mean, and σ is the standard deviation. To find the probability that X is less than 47, we can calculate the z-score for 47 and then use a z-table or a calculator to find the corresponding probability. For X = 47, z = (47 - 50) / 5 = -0.6. Using a z-table, we find that the probability corresponding to a z-score of -0.6 is approximately 0.2743. Therefore, the probability that X is less than 47 is approximately 0.2743.
To find the probability that X is between 47 and 49.5, we can calculate the z-scores for both values and then subtract the probability of the lower value from the probability of the higher value. For X = 47, z = -0.6 (as calculated earlier), and for X = 49.5, z = (49.5 - 50) / 5 = -0.1. Using a z-table, we find that the probability corresponding to a z-score of -0.1 is approximately 0.4602. Therefore, the probability that X is between 47 and 49.5 is approximately 0.4602 - 0.2743 = 0.1859.
To find the probability that X is above 51.1, we can calculate the z-score for 51.1 and then use a z-table or a calculator to find the corresponding probability. For X = 51.1, z = (51.1 - 50) / 5 = 0.22. Using a z-table, we find that the probability corresponding to a z-score of 0.22 is approximately 0.5871. Therefore, the probability that X is above 51.1 is approximately 1 - 0.5871 = 0.4129.
There is no information provided to calculate the probability of a specific value occurring, so we cannot determine the probability of X being a specific value like 35%, Option D. The probability calculations above only apply to specific ranges or values.