Question

forty families gathered for a fund-raising event. suppose the individual contribution for each family is normally distributed with a mean and a standard deviation of $115 and $35, respectively. the organizers would call this event a success if the total contributions exceed $5,000. what is the probability that this fund-raising event is a success? note: round final answer to 4 decimal places.

Answer 1

The probability that the fund-raising event is a success is approximately 0.8729.

Step-by-step explanation:

To find the probability that the total contributions exceed $5,000, we need to calculate the z-score for the value $5,000 using the formula:

z = (x - mean) / standard deviation

Substituting the given values, we have:

z = (5000 - 4600) / 35 = 1.1429

Next, we find the probability corresponding to this z-score using a standard normal distribution table or a calculator. The probability is approximately 0.8729. Therefore, the probability that the fund-raising event is a success is 0.8729.