Question

Given that some normally distributed data has a mean of 787.496 and a standard deviation of 148.722. What is the probability that a randomly sampled datapoint will be less than 967.487?

a) 0.755
b) 0.825
c) 0.905
d) 0.975

Answer 1

To find the probability that a randomly sampled data point will be less than 967.487, we can use the z-score formula. The probability that a randomly sampled datapoint will be less than 967.487 is approximately 0.8841.

Step-by-step explanation:

To find the probability that a randomly sampled data point will be less than 967.487, we can use the z-score formula. The z-score is calculated by subtracting the mean from the datapoint and then dividing by the standard deviation: z = (967.487 - 787.496) / 148.722 = 1.209. Using a standard normal distribution table, we can look up the area to the left of a z-score of 1.209, which is approximately 0.8841. Therefore, the probability that a randomly sampled datapoint will be less than 967.487 is approximately 0.8841.